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## #1 2017-03-14 01:46:05

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Translating sentences into equations

Hello,

I need help with this problem below, I don't know how to translate into a equation. It's the only issue I need help with.

Ted Ming owns two soup and sandwich lunch shops. This year the telephone bill for his Cascade shop was \$650 less than twice the telephone bill for his Santa Clara shop. The total telephone expense for both was \$1804. What was the cost of each shop's telephone service for the year?

The yearly bill for the Santa Clara shop was \$

The yearly bill for the Cascade shop was \$

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## #2 2017-03-14 02:03:11

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

hi Lisa,

Great to hear from you again.

Call the Cascade bill X and the Santa bill Y.

Twice the Santa bill is 2Y and 650 less than that is 2Y - 650.

So one equation is X = 2Y - 650

Can you finish it from here?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2017-03-14 02:09:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Translating sentences into equations

Hi;

Let c be the bill of the Cascade shop

Let s be the bill for the Santa Clara shop

This year the telephone bill for his Cascade shop was \$650 less than twice the telephone bill for his Santa Clara shop.

c = 2 s - 650

The total telephone expense for both was \$1804.

s + c = 1804

So we have two equations to solve simultaneously

c = 2 s - 650

s + c = 1804

Can you solve these two?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #4 2017-03-14 02:14:53

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

I don't know where to start on how to solve those two equations. May you give example on how to do this?

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## #5 2017-03-14 02:27:53

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

You need to eliminate one of the unknowns.  For this example it is easiest to replace the c in the second equation with the value of c from the first like this:

s + (2s - 650) = 1804

From there it is just a single unknown equation.  After you find s you should be able to use the first equation to find c.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #6 2017-03-14 02:41:34

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

Okay now I what to do know with this type of problem, thank you for the help. This example should help me out on my homework. Thanks again!

s + (2s - 650) = 1804

= 818

c = 2 s - 650

= 986

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## #7 2017-03-14 02:43:56

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

I do need help on another question, which is posted below.

Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 38.

Would this consider as a table problem?

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## #8 2017-03-14 02:45:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Translating sentences into equations

Hi;

You should practice on these a bit.

http://www.mathsisfun.com/algebra/syste … tions.html

Would this consider as a table problem?

You can maybe do it like that but the algebraic way is better.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #9 2017-03-14 02:51:43

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 38.

I would call the smaller one N; which makes the larger one N+2

Then make an equation using the information and solve for N

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #10 2017-03-14 02:54:47

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

The equation below is correct?

Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 38.

x + 4x + 2 = 38

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## #11 2017-03-14 03:03:58

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

x + 4(x+2) = 38

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #12 2017-03-14 03:09:46

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

x + 4(x+2) = 38

x + 4x + 8 = 38

5x + 8 = 38

5x + 8 - 8 = 38 - 8

5x = 30

30/5 = 6

So the answer is 6 and 8?

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## #13 2017-03-14 03:11:05

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

Yes!  That's what I made it.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #14 2017-03-14 03:19:49

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

May I do another problem for you? I just want to make sure i do it correctly.

When the smaller of two consecutive integers is added to two times the larger, the result is 17.

x + 2(x + 2) = 17

x + 2x + 4 = 17

3x + 4 = 17

3x + 4 - 4 = 17 - 4

3x = 13

Now how would I get the finally answer since it wouldn't be even?

Last edited by lisathedork (2017-03-14 03:20:35)

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## #15 2017-03-14 03:26:48

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

This time it says the integers are consecutive.  It doesn't say they are even.  So it could be 11 and 12.  Or 3 and 4.

So call the smaller, x and the next (x+1) not (x+2)

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #16 2017-03-14 03:29:19

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

x + 2(x + 1) = 17

x + 2x + 2 = 17

3x + 2 - 2 = 17 - 2

3x = 15

So the answer would be 5 and 6?

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## #17 2017-03-14 03:35:16

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

Yes, that's right.

What I do is see if the answers fit the question.

Twice the second is 2 x 6 = 12.  Add on the first and we get 5 + 12 = 17, which is what we want.  So the answers fit.

Any more?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #18 2017-03-14 03:40:25

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

One more last question, which is posted below:

If the sum of three consecutive even integers is 186, what is the first of three even integers?

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## #19 2017-03-14 03:42:11

lisathedork
Member
Registered: 2013-10-24
Posts: 36

### Re: Translating sentences into equations

Would the equation be something like this

x + 3(x + 1) + (x + 2) = 186

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## #20 2017-03-14 04:42:26

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Translating sentences into equations

This time it does say even integers.  So let them be

x;   x+2;   x+4

Then it says the sum of them so just add them up without any times by 3 for the middle one.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #21 2017-03-14 04:44:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Translating sentences into equations

Hi;

Call the first even integer 2x.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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