Explanation:
Let's first use algebra to find the current number of stamps that Jason and Ashley have.
Let x be the number of stamps that Ashley has.
Then, since the ratio of Jason's stamps to Ashley's stamps is 5:2, we can write:
Jason's stamps = (5/2) * Ashley's stamps
Jason's stamps = (5/2) * x
Jason's stamps = (5x/2)
We also know that Jason has 42 more stamps than Ashley, so we can write:
Jason's stamps = Ashley's stamps + 42
Substituting (5x/2) for Jason's stamps in the above equation, we get:
(5x/2) = x + 42
Solving for x, we get:
x = 28
So Ashley has 28 stamps, and Jason has:
Jason's stamps = (5/2) * 28 = 70
Now we need to find how many stamps Jason should give to Ashley so that the ratio becomes 3:4.
Let y be the number of stamps that Jason gives to Ashley.
After giving y stamps to Ashley, Jason will have:
(70 - y) stamps
And Ashley will have:
(28 + y) stamps
We want the ratio of Jason's stamps to Ashley's stamps to be 3:4, so we can write:
(70 - y)/(28 + y) = 3/4
Cross-multiplying, we get:
4(70 - y) = 3(28 + y)
Simplifying, we get:
280 - 4y = 84 + 3y
Bringing all the y terms to one side and all the constant terms to the other, we get:
7y = 196
Dividing both sides by 7, we get:
y = 28
So Jason should give 28 stamps to Ashley.
After giving 28 stamps to Ashley, Jason will have 42 stamps (70 - 28), and Ashley will have 56 stamps (28 + 28).
The ratio of Jason's stamps to Ashley's stamps is then 42:56, which simplifies to 3:4.