Solve application problems using linear equations.

Question

Randall is 8 years older than Ashley. In 3 years the sum of their ages will be 78. How old is Randall now?

Answer 1

r = a + 8

r + 3 + a + 3 = 78

Suuuubstitute!

a + 8 + a + 3 + 3 = 78

2a = 64

a = 32 years old

r = 32 + 8

y = 40 years old

Answer 2

1. Randall's age is given by R and Ashley's age is given by A.
2. A +8 = R .... Randall is 8 years older ( first equation with 2 unknowns)
3. A+3 +R+3 = 78 .... When they both age 3 more years each, the sum of ages will be 78
4. A + R = 72 .... subtracting 6 from both sides of the equation (second equation with 2 unknowns)
5. A + A + 8 =78 .... substituting R with the left hand side of eq. 2.
6. 2A =70 .... subtract 8 from both sides, and combine the A terms
7. A = 35 .... divide both sides by 2 to get Ashley's age.
8. R = 35 +8 = 43 .... sub Ashley age into eq. 2 to get Randall's age