Question

A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $175 without tax and that the Calculator cost $15 more than four times the cost of the textbook what was the cost of each item?

Answer 1

textbook: $32

calculator: $143

Explanation:

Let x stand for the cost of the calculator. Let y stand for the cost of the textbook.

We know that the total cost for a calculator and a textbook was $175, so write an equation:

x+y=175

And we know that the calculator cost, x, is $15 more than 4 times the cost of the textbook, y. So write an equation:

x=4y+15

Now we have a system of equations:

x+y=175

x=4y+15

To solve said system of equations, we have to find x and y. To do this, input the 2nd equation into the 1st equation like so:

x+y=175

x=4y+15

(4y+15)+y=175

simplify to solve for y

5y+15=175

subtract both sides by 15

5y=160

divide both sides by 5

y=32

y=32, meaning that the cost of the textbook is $32. Now that we know this, we can input 32 into the first equation to solve for x.

x+y=175

x+32=175

subtract 32 from both sides

x=143

So, the calculator costs $143.

We can check this by:

(32·4)+15

=128+15

=143

So, the textbook costs $32 and the calculator costs $143.

Hope this helps! :)