Age word problem: If 3 times Jane's age is equal to....

[Sandi Weot]

If 3 times Jane's age, in years, is equal to 8 times Beth's age, in years, and the difference between them is 15 years, how old are Jane and Beth?

This is what I have so far- J-B=15
The next equation is what I can't figure out. I thought something like this.
3J=8B but I know that's not right.
The answers are 24 and 9. Thanks

 

[stapel]

These can be tricky. It helps to be very, very clear in your labelling and your working:

. . . . .Jane's age now: J
. . . . .Beth's age now: B

. . . . .To get the same value, you have to multiply B by 8
. . . . .but you only have to multiply J by 3. Then J must be
. . . . .the larger number, and Jane is the elder of the two.

. . . . .difference: J - B = 15

. . . . .multiplication: 3J = 8B

(In other words, you're doing just fine so far!)

This gives you two equations in two unknowns. To solve the system, you might find it helpful to rearrange it a bit:

. . . . .1J - 1B = 15
. . . . .3J - 8B = 0

You can solve this fairly quickly using either elimination/addition or substitution.

Eliz.

 

[Denis]

Let's keep it simple:

j = 15+b
8b = 3j ; just substitute:
8b = 3(15 + b)
8b = 45 + 3b
5b = 45
b = ?