Competition · AMC preparation · step 4 of 4
AMC 8 · 2023 · #5
Grade 4 rate-ratioPick an answer.
AMC 8 2023 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Read the sample as a repeating pattern: out of every 180 fish, 30 are trout — that means in every group of 6 fish, exactly 1 is a trout (Tool #5). The whole lake follows the same pattern, so we just count how many groups of 6 fit around the 250 trout we know about. We don't need algebra: scaling a sample to a population is a smaller, friendlier version of the same multiplication problem (Tool #9). Since this is multiple-choice, Tool #3 lets us double-check the answer against the listed options at the end.
Find the sample ratio
Simplify the sample: 30 trout out of 180 fish reduces to 1 trout in every 6 fish.
Recognizing that 30/180 and 1/6 are equivalent fractions is exactly the Grade 4 equivalent-fractions skill.
4.NF.A.1Look For A PatternApply the ratio to the lake
The lake shares that ratio, so its 250 trout mean the lake is built from 250 groups of 6 fish.
"For each trout, there are 6 fish total" is a Grade 4 multiplicative comparison: fish = 6 × trout.
Because the lake shares the sample's trout-to-fish ratio, the lake holds six fish for every trout, so its 250 trout come paired with 250 equal groups of six fish.
▸ Why?
The sample worked out to one trout among every six fish, and the lake is assumed to have that same ratio, so the lake's ratio must also be one trout to six fish.
▸ Why?
With one group of six fish attached to each trout, every one of the 250 trout marks off exactly one group, so the number of groups equals the number of trout.
Multiply for the total
Count them all: 250 groups × 6 fish each gives 1500 fish in the lake.
Multiplying a 3-digit number by a 1-digit number is a Grade 4 fluency standard.
4.NBT.B.5Look For A PatternCheck against the choices
Cross-check the choices: 1500 is (B); the others like = break the ratio.
Checking whether 250/1500 reduces to 1/6 is again the Grade 4 equivalent-fractions check.
4.NF.A.1Eliminate PossibilitiesThis AMC 8 problem only needs Grade 4 equivalent fractions and multiplicative comparison you already know!
- Find the sample ratio
- Apply the ratio to the lake
- Multiply for the total
- Check against the choices
A parent dashboard for the family lives at sensimlab.com.