The larger of two numbers is 20 more than the smaller. Four times the larger is 70 more than 5 times the smaller

Answer 1

x = smaller; y = larger (y>x)

y = x + 20

Four times is larger is 4y; 70 more than five times the smaller is 5x + 70

Set them equal: 4y = 5x + 70

Substitute for y: 4(x + 20) = 5x + 70

Distributive rule: 4x + 80 = 5x + 70

10 = x, then y = 30

Check: 4(30) = 5(10) + 70 (OK, but this assumes the initial equations were set up correctly!)