We are given a balanced scale, which means the total weight on the left side equals the total weight on the right side.
Let’s define:
- Let
B = weight of one blue circle (in grams)
- Let
G = weight of one green square (in grams)
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Left side of the scale:
- 4 blue circles → 4B
- 2 green squares → 2G
→ Total left =
4B + 2G
Right side of the scale:
- 1 blue circle → B
- 1 green square → G
- 1 weight labeled “5g” → 5
→ Total right =
B + G + 5
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Since the scale is balanced:
>
4B + 2G = B + G + 5
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Step 1: Subtract B and G from both sides
> 4B - B + 2G - G = 5
→
3B + G = 5
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This is our key equation:
>
3B + G = 5
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We now need to find values for B and G that satisfy this equation. Since we’re dealing with physical weights and the problem likely expects integer or simple fractional answers, let’s try small positive values.
Try
B = 1:
→ 3(1) + G = 5 → G = 2
That works!
Check if it makes sense:
- Left: 4B + 2G = 4(1) + 2(2) = 4 + 4 =
8
- Right: B + G + 5 = 1 + 2 + 5 =
8 ✔ Balanced!
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Final Answer:
>
Each blue circle weighs 1 gram, and each green square weighs 2 grams.
✔ This satisfies the balance condition.
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Explanation Summary:
We set up an equation based on the balance: total weight left = total weight right. We defined variables for unknown weights, simplified the equation, and solved by testing small integer values. The solution (B=1g, G=2g) balances both sides perfectly.
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Parent Tip: Review the logic above to help your child master the concept of pan balance problems worksheet.
