Lauren is 18 years younger than Joyce. 12 years ago, Joyce was 4 times as old as Lauren was Find their ages.?

Question

With work if you please?

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Answer 1

Let L = Lauren's current age, and J = Joyce's current age, then

Then "Lauren is 18 years younger than Joyce" translates to the equation: L = J-18

"12 years ago, Joyce was 4 times as old as Lauren was" translates to

J-12 = 4(L-12)

Plug in L = J-18 into the second equation.

J-12 = 4(J-18-12)

Solve for J.

J-12 = 4(J-30)

J-12 = 4J - 120

-3J = -108

J = 36 years for Joyce

L = J-18 = 36-18 = 18 years for Lauren

Let's check.

12 years ago, Joyce was 36-12 = 24 years old.

12 years ago, Lauren was 18-12 = 6 years old.

Is Joyce 4 times as old as Lauren at this point?  Yes, because 4(6) = 24.