Question

a student bought a calculator and a textbook for a course in algebra. he told his friend that the total cost was $180 (without tax) and that the calculator cost $25 more than four times the cost of the textbook. what was the cost of each item? let ( x = ) the cost of a calculator and ( y = ) the cost of the textbook. the corresponding modelling system is ( \begin{cases} x + y = 180 \\ x = 4y + 25 end{cases} ) solve the system by using the method of substitution.

answer
how to enter your answer (opens in new window)
enter the ordered pair below.
( , )

Explanation:

Step1: Substitute x into the first equation

We know that \( x = 4y + 25 \) and \( x + y = 180 \). Substitute \( x \) in the first equation with \( 4y + 25 \), so we get \( (4y + 25) + y = 180 \).

Step2: Simplify and solve for y

Combine like terms: \( 5y + 25 = 180 \). Subtract 25 from both sides: \( 5y = 180 - 25 = 155 \). Then divide both sides by 5: \( y=\frac{155}{5}=31 \).

Step3: Solve for x

Substitute \( y = 31 \) into \( x = 4y + 25 \), so \( x = 4\times31 + 25 = 124 + 25 = 149 \).

Answer:

\((149, 31)\)