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Viefleur [7K]
3 years ago
14

Giselle's youth club sells cookies to fund their trips and activities. Each year they need to earn $1,247 from selling cookies.

For each box of cookies they sell, they make $1.45. If Giselle's club has already made $472.70 from selling cookies, how many more boxes do they need to sell to meet their goal?
Mathematics
1 answer:
algol [13]3 years ago
6 0

Price per box, P = $1.45 .

Money left, M = $1247 - $472.70 = $774.3  .

Let, number of boxes are x.

So,

x = \dfrac{774.3}{1.45}\\\\x = 534\ boxes

Therefore, they have to sell 534 more boxes.

Hence, this is the required solution.

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anzhelika [568]
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
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V_{0} = initial investment.
i_{a} = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
V_{0} =(1+ i_{q} ) ^{4}
Where
V_{0} = initial investment.
i_{q} = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
(1+ i_{a} )=(1+ i_{q} ) ^{4}
Notice that we are not using the initial investment V_{0} since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
(1+0.07)=(1+ i_{q} ) ^{4}
1.07=(1+ i_{q} ) ^{4}
\sqrt[4]{1.07} =1+ i_{q}
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i_{q} =0.017
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.


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Answer:

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