the larger of two numbers is one more than four times the smaller number if the sum of the numbers is 106, find the numbers.

Question

i need to set up an equation and solve the equation to find the two numbers values.

Answer 1

Here's what we know:

x + y = 106 (their total is 106)

x = 4y + 1 (the larger is 4-times the smaller plus one)

 

From here we have a substitution method--we have a value for x to plug in:

(4y + 1) + y = 106

Simplify:

5y + 1 = 106

Subtract 1 from both sides:

5y = 105

Divide both sides by 5:

y = 21

 

Now that we know y, we can solve for x:

x = 4 * 21 + 1

x = 84 + 1

x = 85

 

Now to check our answer:

85 + 21 = 106

106 = 106