Question

#8 Dylan, Mike and Jeremy had $171. Mike had twice as much money as Dylan. Jeremy had three times as much money as Mike. How much money did Jeremy have?

#9 we skipped this one


 
#10. Maddy had twice as many stamps as Simon. After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy. How many more stamps did Maddy have than Simon in the beginning?

Answer 1

8. $114

10. 60 stamps

Explanation:

8.

Let Dylan have d, Mike have m, and Jeremy have j

3 of them have 171, so we can write:

1.
`d + m + j = 171`

Mike has twice as Dylan, so we can write:

2. m = 2d

Jeremy had three times as Mike, so:

3. j = 3m

We can write equation 3 as m = j/3

Also, if we put this into equation 2, we have:

j/3=2d

d=j/6

Now we have d and m in terms of j. We put it into equation 1 and solve for j:

`(j)/(6) + (j)/(3) + j = 171\\(3j+6j+18j)/(18)=171\\(27j)/(18)=171\\27j=18*171\\27j=3078\\j=(3078)/(27)\\j=114`

Jaime has $114

10.

amount of stamps Maddy has is m and amount Simon has is s

Maddy had twice as many stamps as Simon:

m = 2s

Also

After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy:

s+60=2(m-60)

We put the first equation in the second and solve for s:

s+60=2(m-60)

s+60=2(2s-60)

s+60=4s-120

180=3s

s=60

THus, m = 2(60) = 120

So maddy had 120 - 60 = 60 more stamps than Simon