Question

a student bought a calculator and a textbook for a course in algebra. he told his friend that the total cost was $160 (without tax) and that the calculator cost $25 more than twice 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 modeling system is ( \begin{cases} x + y = 160 \\ x = 2y + 25 end{cases} ). solve the system by using the method of substitution.

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enter the ordered pair below.

Explanation:

Step1: Substitute \( x = 2y + 25 \) into \( x + y = 160 \)

Substitute the expression for \( x \) from the second equation into the first equation. So we get \( (2y + 25) + y = 160 \).

Step2: Simplify and solve for \( y \)

Combine like terms: \( 3y + 25 = 160 \). Subtract 25 from both sides: \( 3y = 160 - 25 = 135 \). Then divide both sides by 3: \( y=\frac{135}{3}=45 \).

Step3: Find \( x \) using \( x = 2y + 25 \)

Substitute \( y = 45 \) into the equation for \( x \): \( x = 2(45)+25 = 90 + 25 = 115 \).

Answer:

\((115, 45)\)