The average of two numbers is 18. When 2 times the first number is added to 5 times the second number, the result is 120. How do I find the two numbers?

Question

1486 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-17T08:04:58

Express as algebraic equations in two variables $x$ $x$ and $y$ $y$ then use substitution to find:

$x = 20$ $x = 20$

$y = 16$ $y = 16$

Let the two numbers be $x$ $x$ and $y$ $y$ .

We are given:

$\frac{x + y}{2} = 18$ $(x+y)/2 = 18$

$2 x + 5 y = 120$ $2x+5y = 120$

Multiply both sides of the first equation by $2$ $2$ to get:

$x + y = 36$ $x + y = 36$

Subtract $y$ $y$ from both sides to get:

$x = 36 - y$ $x = 36 - y$

Substitute this expression for $x$ $x$ into the second equation to get:

$120 = 2 x + 5 y = 2 (36 - y) + 5 y = 72 - 2 y + 5 y = 72 + 3 y$ $120 = 2x+5y = 2(36 - y) + 5y = 72 - 2y + 5y = 72 + 3y$

Subtract $72$ $72$ from both ends to get:

$3 y = 120 - 72 = 48$ $3y = 120 - 72 = 48$

Divide both sides by $3$ $3$ to get:

$y = 16$ $y = 16$

Then substitute that into $x = 36 - y$ $x = 36 - y$ to get:

$x = 36 - 16 = 20$ $x = 36 - 16 = 20$