Kevin opened a bank account and plans to deposit $200 each month. Each time he makes a deposit, his parents have agreed to add 50% of the amount the family collects for returning cans and bottles.
a) Write an equation that will show his monthly amount when the family collects x dollars of bottle returns.
b) What is the amount when the family collects $27 in bottle returns?
c) If the amount is $223, how much did they collect in bottle returns?
deposit = 200 + .5 x
deposit = 200 + .5(27) = 213.50
223 = 200 + .5 x
.5 x = 23
x = 11.50
I got the same except for the last one.
.5x=23
x=46
a) To write the equation that shows Kevin's monthly amount when the family collects x dollars of bottle returns, we need to consider the $200 he deposits each month and the additional 50% of the bottle returns his parents contribute.
Let's break it down step by step:
- Kevin deposits $200 each month.
- The family collects x dollars in bottle returns.
- Kevin's parents then add 50% of the bottle returns.
To calculate the total monthly amount, we need to add these three components together:
Total Monthly Amount = Kevin's deposit + Kevin's parents' contribution
Kevin's deposit = $200
Kevin's parents' contribution = 50% of the bottle returns = (50/100) * x = 0.5x
The equation for Kevin's monthly amount becomes:
Total Monthly Amount = Kevin's deposit + Kevin's parents' contribution
Total Monthly Amount = $200 + 0.5x
b) To find the amount when the family collects $27 in bottle returns, we can substitute x = $27 into the equation derived in part a:
Total Monthly Amount = $200 + 0.5x
Total Monthly Amount = $200 + 0.5(27)
Total Monthly Amount = $200 + $13.50
Total Monthly Amount = $213.50
So, the amount when the family collects $27 in bottle returns is $213.50.
c) If the amount is $223, we can rearrange the equation derived in part a to find the value of x (the amount the family collected in bottle returns):
Total Monthly Amount = $200 + 0.5x
Substituting the known amount ($223) for the total monthly amount:
$223 = $200 + 0.5x
Next, we can isolate the variable x:
0.5x = $223 - $200
0.5x = $23
To solve for x, we divide both sides of the equation by 0.5:
x = $23 / 0.5
x = $46
So, the family collected $46 in bottle returns.