Translating sentences into equations

lisathedork · 2017-03-14 01:46:05

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 $

Bob · 2017-03-14 02:03:11

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

bobbym · 2017-03-14 02:09:44

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?

lisathedork · 2017-03-14 02:14:53

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

Bob · 2017-03-14 02:27:53

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

lisathedork · 2017-03-14 02:41:34

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

lisathedork · 2017-03-14 02:43:56

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?

bobbym · 2017-03-14 02:45:38

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.

Bob · 2017-03-14 02:51:43

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

lisathedork · 2017-03-14 02:54:47

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

Bob · 2017-03-14 03:03:58

x + 4(x+2) = 38

Bob

lisathedork · 2017-03-14 03:09:46

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?

Bob · 2017-03-14 03:11:05

Yes! That's what I made it.

Bob

lisathedork · 2017-03-14 03:19:49

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)

Bob · 2017-03-14 03:26:48

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

lisathedork · 2017-03-14 03:29:19

x + 2(x + 1) = 17

x + 2x + 2 = 17

3x + 2 - 2 = 17 - 2

3x = 15

So the answer would be 5 and 6?

Bob · 2017-03-14 03:35:16

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

lisathedork · 2017-03-14 03:40:25

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?

lisathedork · 2017-03-14 03:42:11

Would the equation be something like this

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

Bob · 2017-03-14 04:42:26

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

bobbym · 2017-03-14 04:44:54

Hi;

Call the first even integer 2x.

Math Is Fun Forum

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

Translating sentences into equations

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

Re: Translating sentences into equations

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

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

Re: Translating sentences into equations

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

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

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

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