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CaHeK987 [17]
3 years ago
14

Regina spent $45.50 over 612 months on music downloads. If she spent the same amount of money each month, how much money did Reg

ina spend per month on music downloads? Drag numbers to write an equation to represent the situation. Numbers may be used once or not at all.
Mathematics
2 answers:
Flauer [41]3 years ago
5 0
74c a month? Should/Could be the answer
Olenka [21]3 years ago
5 0

Answer:

She spend $0.7435 per month.

Step-by-step explanation:

Consider the provided information.

Regina spent $45.50 over 612 months on music downloads.

she spent the same amount of money each month.

Let she spent x amount each month.

She spent x amount each month for 612 months and in total she spent $45.50

This can be written as: 612x=45.50

Divide both sides by 612.

\frac{612x}{612}=\frac{45.50}{612}

x=0.07435

Hence, she spend $0.0743 per month.

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Use the product-to-sum identity,

\log_x(yz) = \log_x(y) + \log_x(z)

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xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}

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and simplify to

xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)

Now expand the right side:

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}

Simplify and rewrite using the logarithm properties mentioned earlier.

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1

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(C)

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