Question

Write and solve an equation to solve each problem.

Split 84 into two parts so that one part is five × the other part.

a) Lesser number: 12, Greater number: 72
b) Lesser number: 14, Greater number: 70
c) Lesser number: 16, Greater number: 68
d) Lesser number: 18, Greater number: 66

Answer 1

To split the number 84 into two parts where one part is five times the other, we solve the equation x + 5x = 84, resulting in the lesser number being 14 and the greater number being 70.

Step-by-step explanation:

To split the number 84 into two parts so that one part is five times the other, we can set up an equation. Let the lesser number be x and the greater number be 5x. Therefore, the equation to represent their sum as 84 is:

x + 5x = 84

Combining like terms gives us:

6x = 84

Dividing both sides by 6 to solve for x gives us:

x = 14

Therefore, the lesser number is 14, and the greater number is:

5 × 14 = 70

The two parts are 14 and 70.

Checking the sum of these two parts:

14 + 70 = 84, which confirms the solution.