The equation T = 0.03c + 0.05b relates the numbers of cans c and bottles b collected in a recycling rally to the total dollars T raised. How many cans were collected if $147 was raised and 150 bottles were collected? Solve the equation for c and justify each step.
To solve the equation T = 0.03c + 0.05b for c, and find the number of cans collected, we have the values T = $147 and b = 150 bottles.
Step 1: Substitute the given values into the equation.
T = 0.03c + 0.05b
$147 = 0.03c + 0.05(150)
Step 2: Multiply 0.05 by 150.
$147 = 0.03c + 7.5
Step 3: Subtract 7.5 from both sides of the equation.
$147 - 7.5 = 0.03c + 7.5 - 7.5
$139.5 = 0.03c
Step 4: Divide both sides of the equation by 0.03 to isolate c.
$139.5 / 0.03 = 0.03c / 0.03
c = $4650 / 0.03
c = 155,000
Step 5: Therefore, 155,000 cans were collected in the recycling rally.
To find the number of cans collected, we need to solve the equation T = 0.03c + 0.05b for c given that $147 was raised and 150 bottles were collected.
Step 1: Substitute the given values into the equation.
T = 147 (the total dollars raised)
b = 150 (the number of bottles collected)
The equation now becomes:
147 = 0.03c + 0.05 * 150
Step 2: Simplify the equation.
Multiply 0.05 by 150:
147 = 0.03c + 7.5
Step 3: Isolate the variable c.
To isolate c, subtract 7.5 from both sides of the equation:
147 - 7.5 = 0.03c + 7.5 - 7.5
139.5 = 0.03c
Step 4: Solve for c.
To solve for c, divide both sides of the equation by 0.03:
139.5 / 0.03 = 0.03c / 0.03
c = 4650 / 3
c = 1550
Therefore, 1550 cans were collected.