Problem of the Week
Problem C and Solution
A Pressing Issue
Problem
Steve produces apple juice. One day, after pressing many apples, he filled a 45 litre container
with pure apple juice. He found that the taste of the pure mixture was too strong for his liking.
He removed 9 litres of pure apple juice and replaced it with 9 litres of water. The new mixture
still seemed too strong so he removed 9 litres of the mixture and replaced it with 9 litres of
water. Determine the ratio of pure apple juice to water in Steve’s final 45 litre mixture.
Solution
We need to determine the amount of pure apple juice and the amount of water in the final
mixture.
Steve starts with 45 litres of pure apple juice and no water. After removing 9 litres of pure
apple juice and adding 9 litres of water, he has 45 − 9 = 36 litres of pure apple juice and 9
4
9
1
36
= of the new mixture is pure apple juice and
= of the new
litres of water. So
45
5
45
5
mixture is water.
4
1
He then removes 9 litres of the new mixture, of which is pure apple juice and of which is
5
5
4
36
1
1
9
4
water. So Steve removes × 9 =
or 7 litres of pure apple juice and × 9 = or 1 litres
5
5
5
5
5
5
of water.
1
180 36
144
4
Before adding another 9 litres of water he has 36 − 7 =
−
=
or 28 litres of pure
5
5
5
5
5
4
45 9
36
1
apple juice and 9 − 1 =
− =
or 7 litres of water.
5
5
5
5
5
1
36
45 36
81
1
After adding the additional water he has 9 + 7 = 9 +
=
+
=
or 16 litres of
5
5
5
5
5
5
water.
4
1
144 81
The final ratio of pure apple juice to water is 28 : 16 =
:
= 144 : 81 = 16 : 9.
5
5
5
5
∴ the final ratio of pure apple juice to water is 16:9.