Question

Ron Co. sold sweatshirts ($20) and baseball caps ($10). If total sales were $2,860 and people bought 6 times as many sweatshirts as caps, how many of each were sold?

Answer 1

let the total number of sweatshirts sold be S and the total number of baseball caps sold be B
Total sales is the total number of sweatshirts sold times $20 plus the total number of baseball caps sold times 10.
Equation 1: 20S + 10B = 2860
people bought 6 times as many sweatshirts as caps. Which means the number of sweatshirts sold (S) is 6 times caps sold(B)
Equation 2: S = 6B --- substitute S in equation 1 with 6B
=> 20(6B) + 10B = 2860
=> 120B + 10B = 2860
=> 130B = 2860 --- divide both side by 130
=> B = 2860/130
=> B = 22 --- is the number of caps sold.
To find the number of sweatshirts sold we use equation 2
S = 6B --- but we know now B = 22
=> S = 6(22)
=> S = 132

therefore 132 sweatshirts sold and 22 baseball caps sold.