Step by step
The question
Question: share $200 in the ratio 3 to 7.
Share $200 in the ratio 3 : 7
The ratio says how many equal parts each one gets: 3 for the first and 7 for the second.
1st: 3 parts, 2nd: 7 parts
Careful!
3 to 7 does not mean dividing $200 by 3 and by 7.
It counts parts of the same size.
Careful: not $200 ÷ 3, $200 ÷ 7 ✗
1 Count the parts
All together there are 3 plus 7: 10 equal parts.
= 3 + 7 = 10 parts
2 Draw the bar
3 Find one part
10 parts make $200.
So one part is 200 divided by 10: $20.
= 1 part = 200 ÷ 10 = $20
Every part is $20.
4 Find each share
The first share has 3 parts: 3 times 20 is $60.
= 1st: 3 × 20 = $60
The second share has 7 parts: 7 times 20 is $140.
= 2nd: 7 × 20 = $140
So the shares are $60 and $140.
= $60 and $140
5 Check
Let's check.
The shares add up: 60 plus 140 is $200.
60 + 140 = 200
And divided by 20, they give 3 to 7 again.
So the answer is right!
60 : 140 → ÷ 20 → 3 : 7
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= $60 and $140