Question

Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack. The number of $0.45 comic books is 4 more than the number of $0.75 comic books. Find the number of each type in the pack.

Answer 1

The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books

Explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the unknowns or unknown variables are:

x: number of $ 0.45 comic books

y: number of $ 0.75 comic books

Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack. Then the equation that represents this situation is:

x*0.45 + y*0.75= 9

On the other side, the number of $0.45 comic books is 4 more than the number of $0.75 comic books. Then the equation that represents this situation is:

x+4=y

The system of equations to solve is:

`\left \{ {{x*0.45+y*0.75=9} \atop {x+4=y}} \right.`

One way to solve a system of equations is the substitution method, which consists of solving one of the unknowns in one of the equations and substituting its value in the next.

In this case we directly replace the expression of the variable and of the second equation in the first:

x*0.45 + (x+4)*0.75= 9

Solving:

x*0.45 + 0.75*x + 4*0.75= 9

1.2*x + 3=9

1.2*x= 9-3

1.2*x= 6

x= 6÷ 1.2

x=5

Replacing this value in the expression x+4=y you get:

5 +4=y

9=y

The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books