lemonades and two cookies cost $1.50. Two lemonades and five cookies cost $2.70.
How much do one cookie and one lemonade cost?
Five lemonades and (SAT Only)
Let m = lemonades and let c = cookies
5m + 2c = 1.50
2m + 5c = 2.70
multiply top equation by 2
multiply bottom equation by –5
10m + 4c = 3
-10m + -25c = -13.50
-21c = -10.50
c = ½, or 50 cents
Plugging c back in to the first equation:
5m + 2(1/2) = 1.50
5m = .50
m = .10, or 10 cents
Therefore, together a lemonade and a cookie cost 60 cents.
Alternatively, since this problem is looking for the value of (m + c), we can add the two initial equations together:
7m + 7c = 4.20
If we now factor out a 7 on the left:
7(m + c) = 4.207(m + c) / 7 = 4.20 / 7(m + c) = .60
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