There were some apples, oranges and pears in a basket. There are 50% more oranges than apples. The ratio of the number of apples to the number of pears was 5:4.
(a) Find the ratio of the number of apples to the number of oranges to the number of pears.
(b) If there were 56 more oranges than pears, how many fruits were there in the basket altogether?
number of apples ---- x
number of oranges --- 1.5x
number of pears ---- y
x/y = 5/4
5y = 4x
y = 4x/5
a) apples : oranges = x : 1.5x = 1 : 1.5 = 2:3
b) 1.5x - 4x/5 = 56
solve for x
To find the ratio of the number of apples, oranges, and pears, we'll start by assigning variables to represent the number of each fruit.
Let's say the number of apples in the basket is A, the number of oranges is O, and the number of pears is P.
(a) The problem states that there are 50% more oranges than apples, so we can write this as:
O = A + 0.5A
Simplifying this equation:
O = 1.5A
Next, the ratio of the number of apples to pears is given as 5:4, which means:
A/P = 5/4
We can solve this equation for P:
P = (4/5)A
Now, to find the ratio of the number of apples, oranges, and pears, we can substitute the values we've found:
A/O/P = A/(1.5A)/(4/5)A
Simplifying further:
A/O/P = (5/3)/(4/5)
We can simplify this ratio:
A/O/P = (5/3) * (5/4)
A/O/P = (25/12)
So, the ratio of the number of apples to the number of oranges to the number of pears is 25:12.
(b) The problem states that there are 56 more oranges than pears. Using the variables we assigned earlier, we can set up an equation:
O = P + 56
Since we also know the ratio of apples to pears, we can substitute the expression P = (4/5)A into the equation:
O = (4/5)A + 56
To find the total number of fruits in the basket, we can add up the number of each fruit:
Total fruits = A + O + P
Substituting the expressions we have:
Total fruits = A + ((4/5)A + 56) + (4/5)A
Simplifying further:
Total fruits = (9/5)A + 56
Since we don't have a specific value for A, we can't determine the total number of fruits without additional information.