Question

Marta gasto $60 en la compra de cuadernos iguales si cada cuaderno hubiera costado $2 más Marta hubiera adquirido 80 cuadernos menos por los mismos $60 ¿Cuántos cuadernos compró Marta?

Answer 1

`103\ notebooks`

Step-by-step explanation:

The question in English is

Martha spent $60 to buy the same notebooks if each notebook had cost $2 plus Martha would have bought 80 fewer notebooks for the same $60. How many notebooks did Martha buy?

Let

x -----> the cost of each notebook

n -----> number of notebooks that Marta bought

we know that

`nx=60` ----->
`n=(60)/(x)` -----> equation A

`(n-80)(x+2)=60\\\\nx+2n-80x-160=60\\\\n(x+2)-80x=220 ---> equation\ B`

substitute equation A in equation B and solve for x

`(60)/(x)(x+2)-80x=220`

Multiply by x both sides to remove the fraction

`60(x+2)-80x^2=220x`

`60x+120-80x^2=220x`

`-80x^2-160x+120=0`

Using a graphing tool

Solve the quadratic equation

The solution is

x=$0.581

see the attached figure

Find the value of n

`n=(60)/(0.581)=103\ notebooks`