The key idea
A ratio a:b means the amounts are ak and bk for some k. When something is added to only one part, the other part stays fixed; write the new ratio as an equation in k.
The trap
Treating “parts” as actual amounts, or adding to both parts when only one changes.
Can Desmos do it?
The equation in k is quick to solve once it is written down. Writing it is the skill.
College Board skill: Ratios, rates, proportional relationships, and units · Problem-Solving and Data Analysis
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
The ratio of boys to girls in a club is 3:5. There are 24 members in all. How many more girls than boys are in the club?
Show the answer
Answer: 6The members are 3k boys and 5k girls, so 8k=24 and k=3. There are 15−9=6 more girls.
Level 2 · Test level
The ratio of boys to girls in a club is 4:5. After 7 boys join the club and 3 girls leave it, the numbers of boys and girls are equal. How many girls were in the club originally?
Show the answer
Answer: 50Write the original numbers as 4k boys and 5k girls. Then 4k+7=5k−3, so k=10. There were 50 girls.
Level 3 · Beyond the test
A paint mixture is 1 part blue to 4 parts white. How many liters of blue paint must be added to 40 liters of this mixture to make a mixture that is half blue and half white?
Show the answer
Answer: 24The 40 liters contain 51(40)=8 liters of blue and 32 liters of white. Only blue is added, so blue must rise to 32: add 24 liters.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
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