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06 Feb 2021, 05:16
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B
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89% (01:29) correct
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Of the pieces of fruit in a fruit salad, 1/10 are oranges, 1/5 are apples, 1/2 are peaches, and the remaining 8 pieces are grapes. What is the number of oranges in the fruit salad?
(A) 2
(B) 4
(C) 8
(D) 10
(E) 20
(A) 2
(B) 4
(C) 8
(D) 10
(E) 20
06 Feb 2021, 21:30
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Hoozan
In this question, it will be easier to work on decimals or %
So if total fruits are t, then 0.1t+0.2t+0.5t+8=t.......t-0.8t=8.......t=40
So oranges are 0.1t=0.1*40=4.
Another quick method is
If oranges were just 1, then total oranges would be 10 times or 1*10=10.
Other would be 10*1/5=2 and 19*1/2=5.
Total grapes =10-1-2-5=2
But grapes are 8, so total has to be 8*10/2=40, and oranges 40*1/10=4.
If we keep the fractions as it is.
\((1-(\frac{1}{10}+\frac{1}{5}+\frac{1}{2}))t=8\)
\(\frac{2t}{10}=8......t=40\)
Oranges =\(\frac{1}{10}*40=4\)
22 Feb 2021, 23:28
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f=fruit salad=the whole
The sum of the fruits (the parts)=the whole
orange+apple+peach+grapes=fruit salad
\(\frac{f}{10}+\frac{f}{5}+\frac{f}{2}+8=f\)
Multiply by 10 to remove denominators
f+2f+5f+80=10f
8f+80=10f
80=2f
f=40
Oranges=\(\frac{f}{10}=\frac{40}{10}=4\)
B
The sum of the fruits (the parts)=the whole
orange+apple+peach+grapes=fruit salad
\(\frac{f}{10}+\frac{f}{5}+\frac{f}{2}+8=f\)
Multiply by 10 to remove denominators
f+2f+5f+80=10f
8f+80=10f
80=2f
f=40
Oranges=\(\frac{f}{10}=\frac{40}{10}=4\)
B
