jmc

Question

5 green balls and 2 red balls together weigh 10 pounds, and 1 green ball and 4 red balls together weigh 7 pounds. If all red balls weigh the same amount and all green balls weigh the same, then what is the weight of 8 red and 8 green balls together?

Accepted Answer

Find the sum of the weights of a green and a red ball.

As before, we have

5 g + 2 r = 10

and

g + 4 r = 7.

Before solving this system of equations, we note that we seek

8 g + 8 r,

which equals

8 (g + r) .

So, if we can find

g + r,

we can find the total weight of the balls

without finding the weight of each ball .

Looking at our equations, we see a total of

6 g

and

6 r

on the left, so adding the two equations can get us to

g + r .

Adding the equations gives

6 g + 6 r = 17,

and dividing both sides by

6

gives

g + r = \frac{17}{6} .

Therefore, we have

8 g + 8 r = 8 (g + r) = 8 \cdot \frac{17}{6} = \frac{68}{3} pounds .