Answer:
5
Step-by-step explanation:
Margo bought 7 pens for $23.
Some pens are $3 and some $4.
We need to find how many $3 pens she bought.
Let the number of $3 pens be represented by p and let the number of $3 pens be represented by r. So:
p = $3 and r = $4
Now we know 7 pens were purchased so is we add the number of $3 pens purchased to the number of $4 pens purchased, we will get 7.
p + r = 7
We know that the total cost of the pens is $23 so that equation would be found by takign the $3 pen multiplied by the number of $3 pens purchsed added to the $4 pen multiplied by the number of $4 pens purchsed, which equals $23.
$3p + $4r = $23
Now we have 2 equations and 2 unknowns.
p + r = 7
$3p + $4r = $23
Let's solve for r in the first equation.
p + r = 7 Subtract p from both sides.
p - p + r = 7 - p The p on the left cancels.
r = 7 - p
Now that we know r, we can substitute it into the second equation and solve for p.
$3p + $4r = $23
3p + 4( 7 - p) = 23 Multiply it out.
3p + 4*7 - 4*p = $23
3p + 28 - 4p = 23 Combine like terms.
3p - 4p + 28 = 23
- 1p + 28 = 23 Subtract 28 from both sides.
- p + 28 - 28 = 23 - 28
- p = - 5 Divide each side by -1
- p/- 1 = - 5/ - 1 The negative cancels on each side.
p = 5
We can see Margo bought 5 $3 pens.
For fun, let's solve for how many $4 pens she bought. We know p, so we plug it in the first equation and solve for r.
p + r = 7
5 + r = 7 Subtract 5 from each side
5 - 5 + r = 7 - 5
r = 7 - 5
r = 2
So Margo bought 5 $3 pens and 2 $4 pens!
