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40 votes
40 votes
The ratio of the number of pears to the number of oranges in a basket

is 5:3. The rest of the fruits are apples. There are 54 more pears than
oranges and 3 more apples than oranges.
(a) How many pears are there in the basket?
(b) What percentage of the fruits are apples?

User Jimijon
by
2.9k points

1 Answer

24 votes
24 votes

Answer:

(a) 135

(b) 28%

Explanation:

We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.

p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3

p -o = 54 . . . . . there are 54 more pears than oranges

a -o = 3 . . . . . . there are 3 more apples than oranges

__

a)

Multiply the first equation by 3/5o to get ...

3/5p = o

Substitute that into the second equation:

p -(3/5)p = 54

2/5p = 54 . . . . . . simplify

p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears

There are 135 pears in the basket.

__

b)

a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples

a = 84

The percentage of fruits that are apples is ...

apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%

28% of the fruits are apples

User Chris Lieb
by
2.7k points