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Aloysius spends 50% of his income on rent, utilities, and
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02 Jun 2018, 03:41
02 Jun 2018, 03:41
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Question Stats:
75% (00:52) correct
24% (00:41) wrong based on 73 sessions
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Aloysius spends 50% of his income on rent, utilities, and insurance, and 20% on food. If he spends 30% of the remainder on video games and has no other expenditures, what percent of his income is left after all of the expenditures?
(A) 30%
(B) 21%
(C) 20%
(D) 9%
(E) 0%
(A) 30%
(B) 21%
(C) 20%
(D) 9%
(E) 0%
Re: Aloysius spends 50% of his income on rent, utilities, and
[#permalink]
03 Jun 2018, 08:23
03 Jun 2018, 08:23
1
Let us say Aloysius income is x then,
50% is spent on rent
20% is spent on food
Therefore, 70% is spent in total before anything is spent on video games.
Remaining = 100-70 = 30%
Out of this 30% is spent on video games
Therefore, Final Remaining income = 70% of 0.30x = 0.30x * 0.70 = 0.21 or 21%
50% is spent on rent
20% is spent on food
Therefore, 70% is spent in total before anything is spent on video games.
Remaining = 100-70 = 30%
Out of this 30% is spent on video games
Therefore, Final Remaining income = 70% of 0.30x = 0.30x * 0.70 = 0.21 or 21%
Re: Aloysius spends 50% of his income on rent, utilities, and
[#permalink]
11 Jul 2018, 15:49
11 Jul 2018, 15:49
Expert Reply
Explanation
The 50% spent on rent, utilities, and insurance and the 20% spent on food are both percents of the total, so sum the percents: 50% + 20% = 70%. After these expenditures, Aloysius has 30% left.
He then spends 30% of the remaining 30% on video games. 30% of 30% = 0.30 × 0.30 = 0.09, or 9% of the total, so 30% – 9% = 21% of his income remains.
Alternatively, use smart numbers. If Aloysius’s income is $100, he would spend $50 on rent, utilities, and insurance, and $20 on food, for a total of $70. Of his remaining $30, he would spend 30%, or $9, on video games, leaving $21, or 21%, of the original amount.
The 50% spent on rent, utilities, and insurance and the 20% spent on food are both percents of the total, so sum the percents: 50% + 20% = 70%. After these expenditures, Aloysius has 30% left.
He then spends 30% of the remaining 30% on video games. 30% of 30% = 0.30 × 0.30 = 0.09, or 9% of the total, so 30% – 9% = 21% of his income remains.
Alternatively, use smart numbers. If Aloysius’s income is $100, he would spend $50 on rent, utilities, and insurance, and $20 on food, for a total of $70. Of his remaining $30, he would spend 30%, or $9, on video games, leaving $21, or 21%, of the original amount.
