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If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips

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GianKR
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If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips [#permalink] New post   28 Aug 2023, 09:54
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81% (02:09) correct 19% (02:49) wrong based on 73 sessions
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If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips, how many hops are in 140 jumps?

A) 136
B) 144
C) 150
D) 156
E) 162
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E
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If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips [#permalink] New post   28 Aug 2023, 10:45
This question can be solved either using conversion factors or ratios.

Method 1 (using conversion factors):

We can convert jumps into hops as following: 140 jumps x 81 skips/66 jumps x 33 hops/35 skips= 162 hops
Therefore, 140 jumps=162 hops.

Method 2 (using ratios):

The ratio of hops to skips is 35 to 33 and the ratio of skips to jumps is 66 to 81
Using the multiplier 4 in the first ratio, we get the ratio of hops to skips is 140 to 132
And using the multiplier 2 in the second ratio, we get the ratio of skips to jumps is 132 to 162
Therefore, the ratio of hops to jumps is 140 to 162.

Correct answer is E
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Re: If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips [#permalink] New post   28 Aug 2023, 12:26
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GianKR wrote:
This question can be solved either using conversion factors or ratios.

Method 1 (using conversion factors):

We can convert jumps into hops as following: 140 jumps x 81 skips/66 jumps x 33 hops/35 skips= 162 hops
Therefore, 140 jumps=162 hops.

Method 2 (using ratios):

The ratio of hops to skips is 35 to 33 and the ratio of skips to jumps is 66 to 81
Using the multiplier 4 in the first ratio, we get the ratio of hops to skips is 140 to 132
And using the multiplier 2 in the second ratio, we get the ratio of skips to jumps is 132 to 162
Therefore, the ratio of hops to jumps is 140 to 162.

Correct answer is E


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i couldn't understand both the solutions, can you please elaborate a little.
how did 140 jumps equal 162 hops
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Re: If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips [#permalink] New post   28 Aug 2023, 13:23
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shwetasood wrote:
GianKR wrote:
This question can be solved either using conversion factors or ratios.

Method 1 (using conversion factors):

We can convert jumps into hops as following: 140 jumps x 81 skips/66 jumps x 33 hops/35 skips= 162 hops
Therefore, 140 jumps=162 hops.

Method 2 (using ratios):

The ratio of hops to skips is 35 to 33 and the ratio of skips to jumps is 66 to 81
Using the multiplier 4 in the first ratio, we get the ratio of hops to skips is 140 to 132
And using the multiplier 2 in the second ratio, we get the ratio of skips to jumps is 132 to 162
Therefore, the ratio of hops to jumps is 140 to 162.

Correct answer is E


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i couldn't understand both the solutions, can you please elaborate a little.
how did 140 jumps equal 162 hops


shwetasood

We are given the following:
35 skips=33 hops (equation 1)
66 jumps=81 skips (equation 2)
140 jumps= z hops (equation 3)

And we are asked to find z

Using cross multiplication on equation 2 and 3, we get: z hops= (140 jumps x 81 skips)/66 jumps= ((140x81)/66) skips (as the unit jumps will cancel).

Using this new equation and equation 1:
Z hops= ((140x81)/66) skips
33 hops = 35 skips

We get (again using cross multiplication): z hops= (140x81x33)/(35x66)= 162 hops

This is exactly what I did in the first solving method but in one step using the conversion factors detailed in the equations above.

I hope this helps!

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Re: If 35 skips are equal to 33 hops, and 66 jumps are equal to 81 skips [#permalink]
28 Aug 2023, 13:23
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