Numbers & Place Value

Problem

Combine part expressions into one expression

We know there are 12 red marbles. Green marbles are 3 more than red, and yellow marbles are 4 fewer than twice the number of green marbles. We want to find the number of yellow marbles, and we want to capture the whole calculation in a single expression.
Operations
Your answer
How to solve
Strategy Identify Subproblems — Each color is built from the one before it, so we first solve the small parts in order (green from red, then yellow from green). Once we see how each part is computed, we notice the same numbers flowing through and can fold the three steps into one mixed expression with parentheses that records the whole calculation at once.
1STEP 1

Find the green marbles

Green is 3 more than the 12 red marbles, so add 3 to 12.

12 + 3 = 15
2STEP 2

Find the yellow marbles

Yellow is 4 fewer than 2 times the green count. Double 15, then subtract 4.

2 × 15 - 4 = 30 - 4 = 26
3STEP 3

Combine the parts into one expression

Swapping 15 for (12 + 3) folds everything into one expression: 2 x (12 + 3) - 4.

2 × (12 + 3) - 4 = 2 × 15 - 4 = 26
Answer
26 marbles
The answer is a whole number of marbles, which makes sense. Yellow should be the biggest group: green (15) is a bit more than red (12), and yellow is almost double green, so 26 sits sensibly above both. Evaluating the single expression and the step-by-step parts both give 26, so they agree.
Takeaway

Solve each part in order, then nest the parts inside one expression with parentheses so the whole story fits in a single calculation.

  • Find the green marbles
  • Find the yellow marbles
  • Combine the parts into one expression
Where next?
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▶ Practice — 12 problems