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Brums [2.3K]
3 years ago
5

Phyllis paid $408 for new wall-to-wall carpeting in her living room. The carpeting was $12 per square yard, plus a $120 installa

tion charge. How many square yards did she buy?
A. 26 sq yd


B. 34 sq yd


C. 44 sq yd


D. 24 sq yd
Mathematics
1 answer:
kipiarov [429]3 years ago
3 0
.)26

y=12x+120

y=12(26)+120

y=312+120

y=432 (No)

B.)34

y=12x+120

y=12(34)+120

y=408+120

y=528 (No)

C.)44

y=12(44)+120

y=528+120

y=648 (No)

D.)24

y=12x+120

y=12(24)+120

y=288+120

y=408 (Yes)

The other way is setting it equal to...

12x+120=408

Isolate the variable...

12x+120=408
       -120   -120

12x=288

x=24
Thus (D) is you answer!

Hope this helps!
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In a 10 mile race, Janet covered the first 2 miles at a constant rate. She then sped up and rode her bike the last 8 miles at a
xenn [34]

Answer:

0.83\text{ miles per minute}

Step-by-step explanation:

GIVEN: In a 10 mile race, Janet covered the first 2 miles at a constant rate. She then speed up and rode her bike the last 8 miles at a rate that was 0.5 miles per minute faster. Janet's overall time would have been 2 minutes faster had she ridden her bike the whole race at the faster pace.

TO FIND: What was Janet's average speed (in miles per minute) for the whole race?

SOLUTION:

let the speed of Janet in first 2\text{ miles}  =x\text{ miles per minute}

speed of Janet's bike in last 8\text{ miles}  =x\text{+0.5 miles per minute}

total time taken by Janet,

\text{Time}=\frac{\text{distance}}{\text{speed}}

\text{Time taken}=\frac{2}{x}+\frac{8}{x+0.5}\text{minute}

Time taken if Janet rides whole race at faster pace =\frac{10}{x+0.5}\text{minute}

 

As, Janet's overall time would have been 2\text{ minutes} faster had she ridden her bike the whole race at the faster pace.

\frac{2}{x}+\frac{8}{x+0.5}=\frac{10}{x+0.5}+2

\frac{2}{x}-\frac{2}{x+0.5}=2

\frac{1}{x}-\frac{1}{x+0.5}=1

x^{2} +0.5x-1=0

on solving we get

x=0.5\text{ miles per minute}

\text{Time taken}=\frac{2}{x}+\frac{8}{x+0.5}\text{minute}

\text{Time taken}=\frac{2}{0.5}+\frac{8}{1}\text{minute}

\text{Time taken}=\frac{2}{x}+\frac{8}{x+0.5}\text{minute}

\text{Time taken}=12\text{minute}

Average speed =\frac{\text{total distance}}{\text{time taken}}

Average speed =\frac{10}{12}=0.83\text{miles per minute}

Therefore average speed of Janet was 0.83\text{ miles per minute}

4 0
3 years ago
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