Problem
Dividend equals divisor times quotient
Two numbers A and B add up to 10, and they make the equation 8 divided by A equal to B divided by 3. We must find each of A and B.
Operations
Your answer
Watch out Don't stop at a pair that just sums to 10 — you must also check that it makes 8 divided by A equal to B divided by 3.
How to solve
Strategy Guess and Check — Because A and B are small whole numbers that sum to 10, we can list the few sensible pairs and check which one keeps both sides of 8 divided by A equal to B divided by 3 equal. Guess and check fits this bounded set perfectly.
1STEP 1
List the pairs that sum to 10
Since 8 ÷ A must come out even, A is a factor of 8 — the sum-to-10 pairs are (1,9), (2,8), (4,6), (8,2).
(A,B) ∈ {(1,9),(2,8),(4,6),(8,2)}
Grade 3 sense: dividing 8 evenly only works for the factors of 8, so only a few A values are worth trying.
3.OA.A.4Make A Systematic List2STEP 2
Test each pair in the equation
Testing each pair, only A = 4, B = 6 makes 8 ÷ A equal B ÷ 3 (both give 2).
8 ÷ 4 = 2 and 6 ÷ 3 = 2
Grade 3 division: the equation balances only when both quotients come out to the same whole number, 2.
3.OA.B.6Guess And CheckPutting A = 4 and B = 6 into keeps the two sides equal.
Why?
Each side works out to the same number, 2, so the equation balances.
Why?
The left side is 2, because dividing asks what number times 4 makes 8, and .
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
The right side is 2, because dividing asks what number times 3 makes 6, and .
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
Since the left side is 2 and 2 is the right side, the left side must be equal to the right side.
🧱Transitivity of equalityIf the first equals the second and the second equals the third, the first equals the third.
Answer
A = 4, B = 6
Check both conditions: A + B = 4 + 6 = 10 (correct), and 8 divided by 4 equals 2 while 6 divided by 3 equals 2, so the two sides match. Both requirements hold.
Takeaway
Try the few pairs that add to 10 and make 8 divide nicely, and only 4 and 6 keep both sides equal!
- List the pairs that sum to 10
- Test each pair in the equation
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested