Expert: Scott A Wilson - 10/22/2009

Question
Sally wants to buy some accessories for her hair. She can buy two scrunchies and four barrettes for $12.50 or one scrunchie and six barrettes for $12.25. How much does the scrunchie cost that she wants to buy?

Answer
Let S be the scrunchies and B be the batteries.

We are given that 2S + 4B = $12.50 and that S + 6B = $12.25.

Divide the first equation by 2, giving S + 2B = 6.25.
Subtract this from the 2nd, giving S + 6B – S – 2B = $12.25 – $6.25.

Combine like terms, giving 4B = $6.  Divide by 4 to get B = $1.50.

Taking the equation with the 4B in it, we know that 4B = $6, so 2S + $6 = $12.50.

Subtracting $6 from both sides gives us 2S = $6.50.

Dividing both sides by 2 gives us S = $3.25.

If we take S = $3.25 and B = $1.50 and put those both in the 2nd equation, we get
$3.25 + 6($1.50) = $3.25 + $9 = $12.25, and that checks, so that’s the answer is
S = $3.25 and B = $1.50.