Video Transcript
Three friends win 6000 pounds. They decide to share the money in
the ratio three to five to four. Calculate the amount each one
receives.
To answer this question, we’re
going to use a fractional method. By considering the ratio three to
five to four, we want to work out what fraction of the total amount each friend
wins. Now, for ease, we’re going to name
these friends 𝐴, 𝐵, and 𝐶. And the first thing we’re going to
do is add the numbers in our ratio. What this does is tells us the
total number of parts we’re sharing the winnings into. Three plus five plus four is
12. And so we’re sharing this 6000
pounds into 12 parts.
Remember, order matters. So 𝐴 gets three of these parts, 𝐵
gets five, and 𝐶 gets four. In terms of fractions then, we can
say that if there are a total of 12 parts and 𝐴 gets three of these, 𝐴 must get
three twelfths of the winning amount. In fact, we can simplify three
twelfths to a quarter. So 𝐴 gets one-quarter of 6000
pounds. In a similar way, since 𝐵 gets
five of the parts, we know 𝐵 gets five twelfths of the money. Finally, 𝐶 gets four parts. So 𝐶 gets four twelfths of the
money. Four twelfths simplifies to a
third. So 𝐶 gets one-third of 6000
pounds.
We’ll work out then how much 𝐴
gets by finding a quarter of 6000. That’s 6000 divided by four, which
is 1500. We’ll come back to 𝐵 in a moment
because it requires an extra step. But to find a third of 6000, we
divide 6000 by three; that’s 2000. We’ll find for 𝐵 one twelfth of
6000 first. That’s 6000 divided by 12, which is
500. So one twelfth is 500 pounds. Five twelfths will be five lots of
500 pounds. That’s five times 500, which is
2500 pounds. The three friends receive 1500
pounds, 2500 pounds, and 2000 pounds, respectively.
