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# help

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You spend \$20 total on paint and brushes. Paint cost \$4 each and brushes cost \$0.50 each. You buy twice as many brushes as paint. How many brushes and paint did you buy?

Mar 28, 2020

#1
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So to solve this problem, you can make a system of equations

\(x = paint \)

\(y = brushes\)

So for the first equation:

\(4x+0.5y=20\)

Why? Because the total \$ of paint and brushes together equals 20, and paints cost 4 dollars and brushes cost 50 cents.

Then for the second equation:

\(y=2x\)

Why? Because the amount of brushes(y), equals twice the number of paints(x).

Then you can use substitution to solve.

\(4x + 0.5(2x) = 20\)

Here I substituted y( as it equals 2x) into the first equation.

\(4x + x = 20\)

\(5x = 20\)

\(x = 4\)

and if you plug it back in:

\(y = 2(4)\)

\(y = 8\)

So:

You have 4 paints and 8 brushes.

You're welcome!

Mar 29, 2020
edited by Guest  Mar 29, 2020
#3
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p  = paint                    cost \$ 4 p

b = brushes = 2p        cost \$ .5(4p) = p             summed = \$20

4p    +     p     =      20

5p= 20                               p = 4        brushes = 2p = 8

Mar 29, 2020
#4
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Typo:   cost of brushes    .5 (2p) = p

Guest Mar 29, 2020