System of Equations: number of sponges, given total cost and

[Bladesofhalo]

I have to write this problem as a system of equations and solve it using Cramer's rule. I know how to solve it but I cant figure out the system of equations associated with this problem. Can anyone help?

The 24 children in art must choose between paint brushes, which cost $.75, and paint sponges, which cost $.25. You need as many scissors, at $1.50, as paint brushes and sponges put together. Each child gets a pair of scissors. You spend $43 total. How many children chose paint sponges?

 

[stapel]

A good start might be to read the exercise, determine the unknowns, and pick variables for them. Then determine the relationships, and develop equations for them.

This is very similar to word problems you've done in earlier algebra courses, so use similar reasoning. If you get stuck, please reply showing all of your work and reasoning, starting with your unknowns and their variables. Thank you.

Eliz.

 

[Denis]

Re: System of Equations: number of sponges, given total cost

I have to write this problem as a system of equations and solve it using Cramer's rule. I know how to solve it but I cant figure out the system of equations associated with this problem. Can anyone help?

The 24 children in art must choose between paint brushes, which cost $.75, and paint sponges, which cost $.25. You need as many scissors, at $1.50, as paint brushes and sponges put together. Each child gets a pair of scissors. You spend $43 total. How many children chose paint sponges?

I fail to see a system of equations, plus Cramer's rule being necessary, since you can solve directly:

scissors: 24 @ $1.50 = $36

brushes + sponges = 43-36 = $7

since there's a total of 24 of those (b = brushes): .75b + .25(24 - b) = 7

 

[Bladesofhalo]

Appreciate the help stapel and denis, thank you so much.