Question

In 2008, a cure for cancer walk sold 21 pink sponsorships and 10 gold sponsorships for a total of $770. In 2009, the walk collected $840 by selling 7 pink sponsorships and 20 gold sponsorships. What is the cost of one pink sponsorship?

Answer 1

$20

Explanation:

I got it right on the test.

Answer 2

1.
Let the cost of one pink sponsorship be P dollars, and the cost of one gold sponsorship be G dollars.

2.
"In 2008, a cure for cancer walk sold 21 pink sponsorships and 10 gold sponsorships for a total of $770"

means that

21*P ($ per pink sponsorship)+10*G ($ per pink sponsorship)= $ 770,

thus, i) 21P+10G=770

3.

"In 2009, the walk collected $840 by selling 7 pink sponsorships and 20 gold sponsorships."

means that

7*P ($ per pink sponsorship)+20*G ($ per pink sponsorship)= $ 840,

thus, ii) 7P+20G=840

4.
we find P and G by solving the system of linear equations:

i) 21P+10G=770
ii) 7P+20G=840

notice the G's: 20 G = (-2) * 10G

multiply equation i) by -2: -42P - 20G = -1540 and add it to equation ii)

i) -42P - 20G = -1540
ii) 7P + 20G = 840
-------------------------------
-42P+7P = -1540+840
-35P = -700
P=-700/(-35)= 20 ($)

Answer: The cost of one pink sponsorship is $20

Remark: we used the "method by elimination", to solve the system of equations.