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John and Walter have their incomes in the ratio 7 : 5.

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John and Walter have their incomes in the ratio 7 : 5.  [#permalink]

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New post 17 Mar 2017, 05:52
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John and Walter have their incomes in the ratio 7 : 5. The expenses of John, Walter and Nancy are in the ratio 9 : 7 : 4. If Nancy spends $2800 and Walter saves $1100, how much is John’s saving is?

A) $2000
B) $2100
C) $2200
D) $2300
E) $2600
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Re: John and Walter have their incomes in the ratio 7 : 5.  [#permalink]

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New post 17 Mar 2017, 06:53
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vikasp99 wrote:
John and Walter have their incomes in the ratio 7 : 5. The expenses of John, Walter and Nancy are in the ratio 9 : 7 : 4. If Nancy spends $2800 and Walter saves $1100, how much is John’s saving is?

A) $2000
B) $2100
C) $2200
D) $2300
E) $2600

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Re: John and Walter have their incomes in the ratio 7 : 5.  [#permalink]

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New post 17 Mar 2017, 06:54
appu2693 wrote:
vikasp99 wrote:
John and Walter have their incomes in the ratio 7 : 5. The expenses of John, Walter and Nancy are in the ratio 9 : 7 : 4. If Nancy spends $2800 and Walter saves $1100, how much is John’s saving is?

A) $2000
B) $2100
C) $2200
D) $2300
E) $2600

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Option B - 2100

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Re: John and Walter have their incomes in the ratio 7 : 5.  [#permalink]

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New post 27 Jul 2018, 11:39
1
vikasp99 wrote:
John and Walter have their incomes in the ratio 7 : 5. The expenses of John, Walter and Nancy are in the ratio 9 : 7 : 4. If Nancy spends $2800 and Walter saves $1100, how much is John’s saving is?

A) $2000
B) $2100
C) $2200
D) $2300
E) $2600

If given ratios and a "counting number," almost always, start with the counting number and its ratio.

We need John's savings.
Savings = (Income - Expenditures)
We have Nancy's expenditures and a ratio that includes Walter and John.
Start there.

Approach:
• Nancy's expenditures -> Expenditures for all 3
• Walter's savings -> Walter's income
• Walter's income -> John's income
• John's income -> John's savings


(1) Use Nancy to find expenditures for all 3

We have a ratio and a "counting number" for Nancy.
We can find the multiplier in dollars, \(x\)

Expenditure ratio
\(J : W : N\)
\(9x: 7x: 4x\)

Multiplier
Nancy spends \($2,800\)
\(4x=$2,800\)
\(x=$700\)

Expenditures, John and Walter
Use \(x\), multiplier, to calculate J's and W's expenditures

John: \(9x=(9*$700)=$6,300\)

Walter: \(7x=(7*$700)=$4,900\)

Expenditures in dollars
JOHN : WALTER : NANCY
\($6300: $4900 : ($2,800)\)

(2) Use Walter's savings to find Walter's income

Walter's income = (expenditures + savings)
W's savings: \($1,100\)
W's expenditures: \($4,900\)
Walter's income: \(($4,900 + $1,100) = $6,000\)

(3) Use Walter's income to find John's income

Use the income ratio of JOHN : WALTER
to find John's income

Income ratio
\(J : W\)
\(7y: 5y\)

Multiplier
\(W=5y=$6,000\)
\(y=$1,200\)

John's income
\(J=7y=(7*$1,200)=$8,400\)
John's income = \($8,400\)

(4) Find John's savings

John's Savings = (Income - Expenditures)

J's income: \($8,400\)
J's expenditures: \($6,300\)

John's Savings: (Income -Expenditures)
Savings = \(($8,400-$6,300)=$2,100\)

Answer B
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Re: John and Walter have their incomes in the ratio 7 : 5. &nbs [#permalink] 27 Jul 2018, 11:39
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John and Walter have their incomes in the ratio 7 : 5.

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