Last month you spent ​$50 on clothing. This month you spent 110​% of what you spent last month. Set up a proportion to model this situation. How much did you spend this​ month?

Question

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Part 1
Set up a proportion to model this situation. Choose the correct answer below.
A.StartFraction 110 Over 50 EndFraction equals StartFraction x Over 100 EndFraction
StartFraction 110 Over 50 EndFraction
equalsStartFraction x Over 100 EndFraction
B.StartFraction 110 Over 100 EndFraction equals StartFraction x Over 100 EndFraction
StartFraction 110 Over 100 EndFraction
equalsStartFraction x Over 100 EndFraction
C.StartFraction 50 Over x EndFraction equals StartFraction 110 Over 100 EndFraction
StartFraction 50 Over x EndFraction
equalsStartFraction 110 Over 100 EndFraction
D.StartFraction x Over 50 EndFraction equals StartFraction 110 Over 100 EndFraction
StartFraction x Over 50 EndFraction
equalsStartFraction 110 Over 100 EndFraction

Answer 1

To model the situation where you spent \( 110% \) of last month's spending, we can set up a proportion based on the relationship between the amounts spent last month and this month.

You spent \( 50 \) dollars last month, and this month you want to find out how much you spent at \( 110% \) of that.

To express this proportionally, we can write:

\[ \frac{110}{100} = \frac{x}{50} \]

Where:

• \( x \) is the amount spent this month.
• \( 110 \) represents \( 110% \).
• \( 100 \) represents the full amount (which is \( 100% \)).
• \( 50 \) is the amount spent last month.

Now, looking through the provided options, the choice that matches this setup is:

D. \(\frac{x}{50} = \frac{110}{100}\)

Now we can solve for \( x \):

\[ x = 50 \times \frac{110}{100} = 50 \times 1.1 = 55 \]

So, you spent $55 this month.