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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?

Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink]

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14 Feb 2016, 20:02

In 1995 , water usage for Johnsons = w and cost per unit of water = c cw = 800 => w=800/c -- 1

In 1996 , cost per unit of water = 1.5 c Water usage for Johnsons so as to pay same amount as in 1995= w' 1.5c * w' = 800 => w' = 800/1.5c => w' = (2/3c)*800 From 1 and 2 , we get w' = 2/3 w (w-w')/w = 1/3

Answer A
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?

A. 33 1⁄3% B. 40% C. 50% D. 66 2⁄3% E. 100%

Total Bill = Rate * Consumption

If rate increases by 50% and becomes (3/2) of initial Rate, Consumption should become (2/3) of initial consumptions so that the Total Bill remains the same.

Total Bill = (3/2) * Rate * (2/3) * Consumption = Rate * Consumption

(2/3) of the initial consumption means a decrease of 1/3 which is 33.33%.

Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink]

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10 May 2016, 21:27

Can be solved as follows: 1995 total bill = 1996 total bill notice that for this question the absolute amount does not matter .. as it is asking for the % decrease in consumption x-consumption in 19951 y-consumption in 1996 p-price per unit of water in 1995 x*p=(3/2)p*y => x=3/2*y=> y = 2/3*x=> y is 1/3rd less than x. so the consumption should fall by 1/3 , which is equiv. to 33.33% reduction. A

Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink]

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11 May 2016, 01:52

water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio

Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink]

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21 Nov 2017, 20:46

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