Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have?
Number of stamps:
0.37s + 0.09s + 0.025s + 0.52 = 8.28
Solve for s in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28
Step 1: Group the s terms on the left hand side:
(0.37 + 0.09 + 0.025)s = 0.485s
Step 2: Form modified equation
0.485s + 0.52 = + 8.28
Step 3: Group constants:
We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides
0.485s + 0.52 - 0.52 = 8.28 - 0.52
Step 4: Cancel 0.52 on the left side:
0.485s = 7.76
Step 5: Divide each side of the equation by 0.485
0.485s/0.485 = 7.76/0.485
s = 16
Source
Number of stamps:
- Number of 37 cent stamps = s
- Number of 3-cent stamps = 3s
- Number of 5-cent stamps = 0.5s
- 37 cent stamps = 0.37s
- 3-cent stamps = 3 * 0.03 = 0.09s
- 5-cent stamps = 0.5 * 0.05s = 0.025s
- Quarter, 2 dime, 7 pennies = 0.52
0.37s + 0.09s + 0.025s + 0.52 = 8.28
Solve for s in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28
Step 1: Group the s terms on the left hand side:
(0.37 + 0.09 + 0.025)s = 0.485s
Step 2: Form modified equation
0.485s + 0.52 = + 8.28
Step 3: Group constants:
We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides
0.485s + 0.52 - 0.52 = 8.28 - 0.52
Step 4: Cancel 0.52 on the left side:
0.485s = 7.76
Step 5: Divide each side of the equation by 0.485
0.485s/0.485 = 7.76/0.485
s = 16
Source