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4 years ago

McKenna pays $16 per month for a gym membership. In addition, she pays $2 per Pilates class.

Mathematics

2 answers:

Nina [5.8K]4 years ago

7 0

No, it is not the correct amount to be charged.

Step-by-step explanation:

Step 1: Given, the monthly gym membership = $16 and charges for Pilates class = $12. So charges for 12 classes = 2 × 12 = $24
Step 2: Calculate total charges for one month.

Total charges = Gym membership + Pilates classes = 16 + 24 = $40

⇒ So the $52 is an incorrect amount.

True [87]4 years ago

4 0

$16 per month can be changed to 16m where m represents months.

The $2 per Pilates class can be 2p where p represents Pilates classes.

An equation of y = 16m + 2p can be set up, where y represents how much McKenna is charged total for gym membership ($52)

52 = 16m + 2p

We know that McKenna attended 12 Pilates classes, and we also know that McKenna attended 1 month, so we plug this in:

52 = 16(1) + 2(12) (simplify)

52 = 16 + 24 (add 24)

52 = 40

Since this is not equal, $52 is not the correct amount to be charged.

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$Step \; 1: \; Assing \; variable \; for \; the \; unknown \; that \; we \; need \; to \; find.\\Let \; x \; be \; additional \; money \; invested$

$Step \; 2: \; Use \; the \; appropriate \; formula \; of \; simple \; interest \; set \; up \; an \; equation\\Interest \; earned \; each \; year = \; Amount \; invested \times annual \; rate \; of \; interest\\\\Amount \; invested \; in \; 4 \% \; rate \; of \; interest=\$4500\\Amount \; invested \; in \; 5\frac{1}{2}\% \; rate \; of \; interest= \$x\\Amount \; invested \; totally \; in \; 4\frac{1}{2}\% \; rate \; of \; interest = \$(4500+x)$

$Interest \; earned \; in \; 4\% \; interest \; rate\\ = \; 4500(4\%)=180\\Interest \; earned \; in \; 5\frac{1}{2}\% \; interest \; rate\\ = x(5\frac{1}{2}\%)=0.055x\\Interest \; earned \; totally \; in \; 4\frac{1}{2}\% \; interest \; rate = (4500+x)(4\frac{1}{2}\%)\\=0.045(4500+x)$

$\\\\So, \; the \; equation \; would \; be:\\180+0.055x=0.045(4500+x)$

$Step \; 1: \; Distribute \; 0.045 \; in \; the \; right \; side\\180+0.055x=202.5+0.045x\\\\Step \; 2: \; Subtract \; 0.045x \; and \; 180 \; on \; both \; sides \; to \; get \; x \; alone\\0.055x-0.045x=202.5-180\\\\Step \; 3: \; Combine \; Like \; Terms\\0.01x=22.5\\\\Step \; 4: Divide \; 0.01 \; on \; both \; sides\\\frac{0.01x}{0.01}=\frac{22.5}{0.01}\\\\Step \; 5: \; Simplifying \; fraction \; on \; both \; sides\\x=2250$

$\underline{Conclusion:}\\Ben \; should \; invest \; additional \; money \; of \; \$2250$

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