Chang Learning SHSAT Lesson #7 - Ratio Problems

Sep 15, 2026

SHSAT Mathematics Lesson #7 focuses on solving ratio word problems with multiple variables by organizing given relationships into clear charts. Model Problem #1 uses a rabbits-cats-dogs situation and applies LCM scaling to combine separate ratio facts into one consistent set, then uses the total to determine actual counts. Model Problem #2 uses a boys-to-girls ratio, sets up an equation with a variable, and solves for x to fill the table and obtain both numbers. Classwork includes additional ratio and fraction-based problems on quantities, mixtures, costs, and multi-step comparisons.

LanguageEnglish

CategoryExam

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Model Problem #1: Ratio of Animals

Step 1: Use a Chart

Step 2: Use the Total to Solve

Model Problem #2: Ratio of Boys to Girls

Set Up with Variable x

Complete the Table and Solve

SHSAT Lesson #7 Classwork: Ratio Problems

Name: Date: Chang Learning SHSAT Lesson \#7: Ratio Problems Ratio Problems When you are given a ratio problem with 2 or more variables, it’s good to have a method to sort the information in a useful chart. Model Problem \#1: At an Animal Shelter, there are 4 Rabbits for every 9 Cats. Also there are 3 Dogs for every 1 Rabbit. If there are 400 animals total, how many Rabbits, Cats, and Dogs are there at the shelter? Solution: Step 1: Use a Chart with a column for each animal. | | Rabbits | Cats | Dogs | | --- | --- | --- | --- | | (Fact 1 :) Rabbits to Cats = 4 :9 | 4 | 9 | | | (Fact 2) Dogs to Rabbits = 3 : 1 | 1 | | 3 | Since we have information for Rabbits in both Facts, we will use the LCM for this column to find the ratio of all three. The LCM is 4. Leave the first row, but multiply row two by four. | | Rabbits | Cats | Dogs | | --- | --- | --- | --- | | (Fact 1 :) | 4 | 9 | | | (Fact 2) Multiply by 4 | (4) * 1 | | (4) * 3 | | Ratio of All Animals | 4 | 9 | 12 | Step 2: Since there are 400 animals total, we know that the total is a multiple of the ratio above. 4􀕠 + 9􀕠 + 12􀕠 = 400. 25􀕠 = 400. 􀕠 = 16 | | Rabbits | Cats | Dogs | Total | | --- | --- | --- | --- | --- | | Ratio of All Animals | 4x | 9x | 12x | 400 | | Ratio times 16 | 4*16=64 | 9*16=144 | 12*16=192 | 400 | Answer: There are 64 Rabbits, 144 Cats and 192 Dogs at the Animal Shelter. SHSAT Mathematics Lesson \#7 Page 1 Name: Date: Chang Learning SHSAT Lesson \#7: Ratio Problems Model Problem \#2: The ratio of boys to girls in all of Mr. Jefferson’s classes is 6 :5. If there are 165 students total at school, how many are boys? How many are girls? | | Boys | Girls | Total | | --- | --- | --- | --- | | Ratio of Boys to Girls = 6 :5 | 6 | 5 | | | All Students | | | 165 | Since we know that the total is a multiple of the ratio, we can use variable “x” to set up an equation. Complete the table, showing that the total of the ratio 6 :5 is 6+5 = 11 also. | | Boys | Girls | Total | | --- | --- | --- | --- | | Ratio of Boys to Girls = 6 :5 | 6 | 5 | 11 | | All Students | 6x | 5x | 165 | 6􀕠 + 5􀕠 = 165 11􀕠 = 165 􀕠 = 15 Since the multiple is 15, we can complete the “All Students” row by plugging in x=15. | | Boys | Girls | Total | | --- | --- | --- | --- | | Ratio of Boys to Girls = 6 :5 | 6 | 5 | 11 | | All Students | 90 | 75 | 165 | Answer: There are 90 Boys. There are 75 Girls. SHSAT Mathematics Lesson \#7 Page 2 Name: Date: Chang Learning SHSAT Lesson \#7: Ratio Problems SHSAT Lesson \#7 Classwork: Ratio Problems | 1. A certain type of drinking glass holds exactly ~~ ~~58~~ ~~ liter of water. How many of those glasses can be filled if you have 40 liters of water ? | A. 72
B. 64
C. 30
D. 25
E. 24 | | --- | --- | | 2. The ratio of boys to girls at a dance was 2 to 3. If 45 girls attended, what is the number of boys who attended ? | A. 9
B. 18
C. 27
D. 30
E. 45 | | 3. There are 420 field mice in a cage. For every 5 gray mice, there are 2 white mice. How many gray mice are there? | A. 240
B. 270
C. 285
D. 300
E. 330 | | 4. A fish tank is fed ⅜ of a pound of fish food every day. For how many days will 15 pounds of this fish food feed the tanked fish? | A. 16 days
B. 20 days
C. 24 days
D. 36 days
E. 40 days | | 5. Thirty of the fifty students who took an exam received a grade of 90% or greater. What percentage of those fifty students received a grade of less than 90% ? | A. 70
B. 35
C. 40
D. 30
E. 10 | | 6. Three river rafters each have a camping bag. The capacities of the bags are in the ratio of 3:4:6 . The total weight of the three bags is 260 pounds. How much does the lightest bag weigh? | A. 30
B. 42
C. 56
D. 60
E. 70 | SHSAT Mathematics Lesson \#7 Page 3 Name: Date: Chang Learning SHSAT Lesson \#7: Ratio Problems SHSAT Lesson \#7: Classwork (continued) | 7. A pet goat eats 3 pounds of grass and 1 pound of“chunky

FAQs

How does the lesson handle ratio problems with more than two variables?

It converts each given relationship into a chart, then uses LCM-based scaling to align the different ratios into a single combined ratio before solving with the total.

What method is used to solve the boys-to-girls ratio problem?

The lesson uses a variable x to represent the common multiplier, sets up an equation using the total number of students, and solves for x to find boys and girls.

What kinds of topics appear in the classwork questions?

The classwork includes drinking glasses and volume, boy-girl attendance ratios, animal counts with proportions, food and time rates, percentage comparisons, and cost/value ratios that require multi-step fraction reasoning.

Sep 15, 2026

Uploaded by Felix Montgomery