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 $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 modeling system is {x + y = 100, x = 4y + 25}. solve the system by using the method of substitution. enter the ordered - pair below.

Explanation:

Step1: Substitute x in the second - equation

Given $x = 4y+25$ and $x + y=100$, substitute $x$:
$(4y + 25)+y=100$

Step2: Combine like - terms

$4y+y+25 = 100$, which simplifies to $5y+25 = 100$.

Step3: Isolate the term with y

Subtract 25 from both sides: $5y=100 - 25$, so $5y=75$.

Step4: Solve for y

Divide both sides by 5: $y=\frac{75}{5}=15$.

Step5: Solve for x

Substitute $y = 15$ into $x = 4y+25$, then $x=4\times15 + 25=60 + 25=85$.

Answer:

(85, 15)