Question

Alex was visiting his uncle joe for summer break. Combined they are 70 years old. Uncle joe is four times as old as alex is. Write a equation that models how old alex and uncle joe are and determine their ages.

Answer 1

Alex is 14 years old and Uncle Joe is 56 years old.

Explanation:

We can arm a system of two equations with two unknowns.

J= uncle joe's age.

A=alex's age.

`\left \{ {{J+A=70} \atop {J=A.4}} \right.`

A system of two equations can be resolved using various methods. I will resolve it using the substitution method, where I will be replacing the value of J=A.4 on the first equation. Then I get:

`A.4+A=70\\5A=70\\A=70:5\\A=14`

Now I know that Alex is 14 years old. If the Uncle joe's age is four times Alex's age, then we know that:

`J=14.4=56`