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Harrizon [31]
3 years ago
15

Toni and Marcy partnered together in running laps around a track to raise money for the Children's Hospital's playroom. Toni rai

sed $20 plus $0.80 per lap that he ran. Marcy raised $15 plus $0.85 per lap that she ran. Toni swam 114114 times as many laps as Marcy swam. Together they raised a total of $257.00. Let x represent the number of laps Marcy swam
Enter the simplified equation that represents the total number of laps Toni and Marcy swam in the first box and the amount of laps Toni swam in the second box.

= 257
Mathematics
1 answer:
lutik1710 [3]3 years ago
3 0
X represent the number of laps Marcy swam, 114x represent the number of times Toni swam.

20 + 0.80(114x) + 15 + 0.85x = 257
20 + 91.2x + 15 + 0.85x = 257
92.05x + 35 = 257

Required equation is 92.05x + 35 = 257
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To solve this we are going to use the future value of annuity ordinary formula: FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]
where
FV is the future value
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n is the number of times the interest is compounded per year
k is the number of payments per year
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We know for our problem that P=6200 and t=5. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
r= \frac{6}{100} =0.06
Since the deposit is made semiannually, it is made 2 times per year, so k=2.
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Lets replace the values in our formula:

FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]
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FV=71076.06

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