Question

Solve the problem by defining the unknown variable, show any formula used, set up an

equation and show all work. Problems must be shown algebraically to receive credit.
7.
7.
A second number is 10 more than three times a first number
The third number is 14 more than six times the first number
The sum of the three numbers is 134. What are the three
numbers?
(a) Define the numbers algebraically by filling in the chart
First number
Second number =
Third number =
(b) Set up and solve an algebraic equation to represent this situation.

Answer 1

11, 43, 80

Explanation:

A second number is 10 more than three times a first number

The third number is 14 more than six times the first number

The sum of the three numbers is 134. What are the three

numbers?

call the first number " x "

call the second number " y "

call the third number " z "

now represent the given information algebraically

y - 10 = 3x

manipulate for the problem:

y = 3x +10

z - 14 = 6x

manipulate for the problem:

z = 6x +14

x + y + z =134

now use substitution to form one equation

x + y + z = 134

x + 3x + 10 + 6x + 14 = 134

simplify and solve by inverse operations:

10x + 24 = 134

10x = 110

x = 11

now substitute back into to find the answer to the problem

y= 3x + 10

y = 3 * 11 +10

y = 43

z = 6x + 14

z = 6 * 11 + 14

z = 80