I need help with Algebra 1 I really do not want to fail.

Question

The larger of two numbers is one more than four times the smaller number. If the sum of

the numbers is 106,what are the numbers?

Answer 1

Hello, Keli,

We have two unknowns, so we need at least two equations.

Let L and S represent the Large and Small numbers.

We are told that "larger of two numbers is one more than four times the smaller number." Write that as an equation:

L = 4S + 1

We also know that the sum of the two is 106:

L + S = 106

Substitute the first equation into the second and replace the L:

(4S + 1) + S = 106

5S + 1 = 106

5S = 105

Therefore S = 21. Use the value for S in the second equation:

L + S = 106

21 + S = 106

L = 85

85 + 21 = 106 : That checks OK

and 4*21 + 1 = 85 : That also works

The two numbers are 85 and 21.

I hope this helps. It was fun.

Bob

Answer 2

x = larger number

y = smaller number

x = 4y + 1 (larger number is one more than 4 times the smaller)

x + y = 106 (sum of two numbers is 106)

substitute 4y+1 for x in second equation:

4y + 1 + y = 106

5y = 105

y = 21

substitute 21 for y in second equation to solve for x

x + 21 = 106

x = 85