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
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-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.
