   SEARCH HOME Math Central Quandaries & Queries  Question from Maya: Two numbers have a sum of 57. Three times the first number is 13 less than the second number. Find the numbers. Use let statements to help you solve. (Grade 9 math) -Maya (help would be appreciated) Hi Maya,

The problem is about two numbers, the first number and the second number. To write this question using mathematical notation I am going to replace the phrase "the first number" by the letter $x$ and the phrase "the second number" by the letter $y.$ To do this I would say

Let $x$ be the first number and $y$ be the second number.

The first statement in the problem "Two numbers have a sum of 57." then become

$x + y = 57.$

The second statement is "Three times the first number is 13 less than the second number." Three times the first number is $3 \times x$ which is 13 less then $y.$ So you need to subtract 13 from $y$ to get to $3 \times x.$ hence

$3x = y - 13.$

Solve this pair of equations for $x$ and $y.$ Make sure you verify your answer.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.