Question

A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $170(without tax) and thatthe calculator cost $30 more than thrice the cost of the textbook. What was the cost of each item? Let x = the cost of a calculator andy = the cost of the textbook. The corresponding modeling system isx + y = 170Solve the system by using the method ofx = 3y + 30substitution.

Answer 1

Given:

x + y = 170.........Equation 1

x = 3y + 30........Equation 2

Asked: Find the value of x and y.

Solution:

First, let's find he value of y.

`\begin{gathered} x+y=170\text{ }\Rightarrow Eqn\text{ 1} \\ x=3y+30\text{ }\Rightarrow Eqn\text{ 2} \\ We\text{ will substitute equation 2 to equation 1.} \\ 3y+30+y=170\text{ } \\ 4y+30=170 \\ 4y=170-30 \\ 4y=140 \\ (4y)/(4)=(140)/(4) \\ y=35 \end{gathered}`

Now, for the value of x, let's substitute y to the second equation.

`\begin{gathered} x=3y+30\text{ }\Rightarrow Eqn\text{ 2} \\ x=3(35)+30\text{ } \\ x=105+30 \\ x=135 \end{gathered}`

ANSWER: (135, 35)

x = 135

y = 35