Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Simultaneous Equations

Exercises
Solve all the values of the pronumerals for all of the pronumerals. Leave answers in improper fractions:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

Last edited by Toast (2006-12-11 21:05:59)

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Simultaneous Equations

Worded Problems - To be answered in full literate sentences.
1. Two numbers have a sum of 42 and a difference of 3. Find the two numbers.
2. Two numbers have a sum of 114. One number is two less than the other. Find both numbers.
3. Shane and James each think of a number. The number Shane thinks of is thrice James' number and the sum of the two numbers is 64. What numbers did they think of?
4. The sum of two numbers is 38. Three times one number less twice the other number is 2. Find the two numbers.
5. At present, Lauren is 25 years older than her son. In 10 years time she will be 3 times as old as her son. What are their ages?
6. Four years ago Brad was twice as old as Dan. In four years time, Brad will be one and a third times older than Dan. How old are they both?
7. George is presently three times as old as his son. In 14 years time, he will be twice as old as his son. How old is George now?
8. Ralph has $16.00 to spend. He can buy either 4 cans of soft drink and 4 chocolate bars or 2 cans of soft drink and 7 chocolate bars. How much does each item cost?
9. Sally buys 3 hamburgers and 5 buckets of chips, spending $15.60. Neo buys 4 hamburgers and 2 buckets of chips and spends $12.40. How much does a hamburger cost?
10. An army transport aeroplane can carry 5 tonnes. It can transport either 21 men and 15 pieces of equipment, or 35 men and 11 pieces of equipment. What is the average weight of the men?
11. At a clohing store, jeans cost twice as much as shirts. Graham purchases 4 shirts and 2 pairs of jeans for a total cost of $240. How much does each shirt cost?
12. The length of a paddock is 10 metres longer than twice its width. If the perimeter of the paddock is 154 metres, find the paddock's dimensions.
13. The equal sided of an isosceles triangle are 5cm longer than the base. If the perimeter of the triangle is 34cm, find the side lengths of the triangle.
14. Sam thinks of a two digit number. The sum of the digits is 8. If he reverses the digits the new number is 36 greater than his original number. What is Sam's original number?
15. Selphie thinks of a fraction. If she adds 4 to both the numerator and the denominator, the fraction is equal to

. If she subtracts 5 from both the numerator and the denominator, the fraction is dqual to

. What fraction did she think of?
16. Find a fraction which is equal to

if 10 is added to both the numerator and the denominator and is equal to

if 5 is subtracted from both the numerator and the denominator.
17. A secretary buys a number of 45c and 60c stamps for a total cost of $22.50. If she interchanged the number of each type of stamp, the total cost would have been $23.70. How many of each type of stamp did she originally buy?
18. On one of the escalators at JFK Airport, Tony finds that if he walks down 26 steps he needs 30 seconds to get to the bottom, but if on another trip he makes 34 steps, then he needs only 18 seconds to reach the bottom.
a) i) Show that if the escalator is stationary, Tony will have to walk 46 steps to get to the bottom.
  ii) How many seconds does it take the escalator to travel one step?
Andy decides to do yet another trip on the escalator. Just as he gets on the escalator, Ronald starts walking up the same escalator from the bottom.
b) i) If Tony walks at a speed of 1 step per second and Ronald walks at a speed of 2 steps per second, after how many seconds will they meet on the escalator?
   ii) Instead, Ronald walks 2 steps per second faster than Tony. It takes 16 seconds before they meet on the escalator. Calculate Tony's walking speed.

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Simultaneous Equations

Last edited by Toast (2007-01-25 18:32:57)

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Simultaneous Equations

Last edited by Toast (2006-12-11 21:08:29)

littlelittle

Member

Registered: 2007-01-24

Posts: 10

Re: Simultaneous Equations

Hi

I got all the answers for the 1st set of problems excepting problem 12.  The answer i am getting is x = -2 and y = 1.

Can you please let me know where i am wrong.

-3x-2y=4
  x+7y=5 (multiply with 3)
=3x+21y=15 (cancel -3x and +3x)
19y = 19 (remains
y = 19/19
y = 1

x+7=5
x = 5-7
x = -2

Thanks so much
S

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Simultaneous Equations

Sorry littlelittle, you're right, I don't know how I messed up the answers for that one, I've changed the answers so they're right now.

littlelittle

Member

Registered: 2007-01-24

Posts: 10

Re: Simultaneous Equations

Sorry - no way.  Pl don't say that.

Thanks so much for taking the time out.

Have a gr8 wkend.
S