Mrs Bruce lacks 1 year from being 5 times as old as her son. Five years from now she will lack 1 from being 3 times as old as her son will be then. Find each of their ages. I know the first equation is x+1= 5y and I know to substitue x = 5y - 1 in the second equation. But I can't figure out the second equation.

Let's say x is Mrs. Bruce's age and y is her son's. Then right now x=5y-1. In five years (x+5), she will be 3(y+5)-1 or:

x+5=3y+15-1=3y+14.

Substituting the equation for x into here that's:

5y-1+5=3y+14

2y=10

y=5

and x=24

Checking our work, in five years, her son will be ten and she will be 29. Check!

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