A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $105
(without tax) and that the calculator cost $25
more than thrice 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=105x=3y+25
. Solve the system by using the method of substitution.
From the first equation, we have x + y = 105.
From the second equation, we have x = 3y + 25.
Now, we can substitute the value of x from the second equation into the first equation.
3y + 25 + y = 105.
Combining like terms, we get 4y + 25 = 105.
Subtracting 25 from both sides, we get 4y = 80.
Dividing both sides by 4, we get y = 20.
Now, we can substitute the value of y into the second equation to find x.
x = 3*20 + 25.
Simplifying, we get x = 60 + 25 = 85.
Therefore, the cost of the calculator is $85 and the cost of the textbook is $20.