Answer:
<em>9</em>
Step-by-step explanation:
Let c = number of chocolate chip muffins.
Let a = number of oatmeal muffins
Let r = number of cranberry muffins
He bought 17 muffins, so
c + a + r = 17
Using the prices, the following equation shows how much he spent,
0.15c + 0.2a + 0.25r = 3.70
Charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins.
r = 3c
We substitute 3c for r in the first two equations.
c + a + r = 17
c + a + 3c = 17
a + 4c = 17 Eq. 1
0.15c + 0.2a + 0.25r = 3.70
0.15c + 0.2a + 0.25(3c) = 3.70
0.15c + 0.2a + 0.75c = 3.70
0.2a + 0.9c = 3.70
2a + 9c = 37 Eq. 2
Equations 1 and 2 are two equations in two unknowns.
a + 4c = 17
2a + 9c = 37
Multiply the first equation just above by -2 and add it to the second equation.
-2a - 8c = -34
+ 2a + 9c = 37
-----------------------
c = 3
r = 3c = 3(3) = 9
9 cranberry muffins
