Question

a student bought a calculator and a textbook for a course in algebra. he told his friend that the total cost was $100 (without tax) and that the calculator cost $15 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 modeling system is \\(\

$$\begin{cases} x + y = 100 \\\\ x = 4y + 15 \\end{cases}$$

\\). solve the system by using the method of substitution.

answer
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Explanation:

Step1: Substitute \( x = 4y + 15 \) into \( x + y = 100 \)

Substitute the expression for \( x \) from the second equation into the first equation. So we get \( (4y + 15) + y = 100 \).

Step2: Simplify and solve for \( y \)

Combine like terms: \( 4y + y + 15 = 100 \) which simplifies to \( 5y + 15 = 100 \). Subtract 15 from both sides: \( 5y = 100 - 15 = 85 \). Then divide both sides by 5: \( y=\frac{85}{5}=17 \).

Step3: Substitute \( y = 17 \) back into \( x = 4y + 15 \)

Calculate \( x \): \( x = 4\times17 + 15 = 68 + 15 = 83 \).

Answer:

\((83, 17)\)