Operations & Word Problems

Problem

Solve shape-coded products in order

Three shapes stand for three different one-digit numbers. From the equations circle x circle = 36, triangle x circle = 48, and square x 2 = the two-digit number '1 triangle', find the sum circle + triangle + square.
Operations
Your answer
How to solve
Strategy Eliminate Possibilities — Solve in order from the equation that can be determined alone: the square of circle pins circle, then triangle follows, then square. Each step has only one valid one-digit value.
1STEP 1

Find the circle

circle x circle = 36, and the only one-digit number that times itself makes 36 is 6.

6 × 6 = 36
2STEP 2

Find the triangle

triangle x circle = 48 and circle = 6, so triangle x 6 = 48, giving triangle = 8.

▲ × 6 = 48 → ▲ = 8
3STEP 3

Find the square and sum

Since triangle = 8, '1 triangle' is 18, so square x 2 = 18 gives square = 9; the distinct shapes 6, 8, 9 sum to 23.

■ × 2 = 18 → ■ = 9, 6+8+9 = 23
Answer
23
Check all three: 6 x 6 = 36, 8 x 6 = 48, and 9 x 2 = 18 = '1 triangle' with triangle = 8; the shapes 6, 8, 9 are distinct one-digit numbers, so the sum 23 is correct.
Takeaway

Start with the shape you can pin down, then unlock the rest in order -- just Grade 3 multiplication facts!

  • Find the circle
  • Find the triangle
  • Find the square and sum
Where next?
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