Depth · one concept from first principles · step 2 of 4
Scaling both terms keeps the ratio
The ratio of Jua's allowance to Eunwoo's is , and Eunwoo received won more than Jua. How much did Eunwoo receive?
RatiosExpressions
Your answer
How to solve
Strategy Convert to Algebra — Read the ratio as equal parts: Jua has seven of them and Eunwoo nine, so the difference is two parts. That turns the 500 won into the size of one part, and everything else follows.
1STEP 1
Read the ratio as parts
Both allowances are made of parts of the same size -- seven for Jua and nine for Eunwoo.
9 - 7 = 2
The difference is 2 parts.
6.RP.A.3Convert To Algebra2STEP 2
Find the size of one part
Those two parts are the 500 won difference.
500 ÷ 2 = 250
Each part is 250 won.
6.EE.B.7Work BackwardsOne part is won.
Why?
The ratio says both allowances are made of the same size part, seven of them and nine of them.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Taking seven parts away from nine leaves two, so the won difference is two parts and one part is half of it.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Count Eunwoo's parts
Eunwoo has nine parts.
250 × 9 = 2250
Eunwoo received 2250 won.
6.RP.A.3Identify SubproblemsAnswer
2250 won
Check both facts: Jua has 250 × 7 = 1750 won, the difference is 2250 - 1750 = 500 won, and 1750 : 2250 reduces to 7 : 9.
Takeaway
Read a ratio as equal parts -- then a difference tells you what one part is worth.
- Read the ratio as parts
- Find the size of one part
- Count Eunwoo's parts
Where next?
Another one like thissuggested
Step back and solidifysuggested
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