Question

The problem solving template is a tool which can be used to help solve difficult problems. For thissample work you will use the problem solving template to set up and then solve the equation. Completeeach part of the template for the question and then solve the question with work shown in the “Do”square.Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 timesthe smaller. If 3 times the larger number is increased by 4 times the smaller, the result is 16.Find the numbers by solving algebraically. Show your work including the equations.

Answer 1

Let the larger number be x.

The smaller number be y.

According to the question,

$x=5y+18\ldots.(1)$$3x+4y=16\ldots.(2)\text{ }$

Putting x from (1) in (2) we have,

$3(5y+18)+4y=16$$19y+54=16$$19y=-38$$y=-2$

Putting y in (1) we have,

$x=5\times(-2)+18=8$

The numbers are 8,-2.