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A bag contains 130 jelly beans - HSC - SSCE Mathematics Standard - Question 13 - 2023 - Paper 1

Question 13

A bag contains 130 jelly beans. Some of them are red and the rest are blue. The ratio of red to blue jelly beans is 2:3. Sophie eats 10 of each colour. What is the... show full transcript

Worked Solution & Example Answer:A bag contains 130 jelly beans - HSC - SSCE Mathematics Standard - Question 13 - 2023 - Paper 1

Step 1

Calculate the initial number of red and blue jelly beans

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Answer

Given the ratio of red to blue jelly beans is 2:3, we can let the number of red beans be represented as $2x$ and the blue beans as $3x$ . The total number of jelly beans is 130:

$2x + 3x = 130$

This simplifies to $5x = 130$ , therefore:

$x = 26.$

Thus, the initial counts are:

Red jelly beans: $2x = 2 \times 26 = 52$
Blue jelly beans: $3x = 3 \times 26 = 78$ .

Step 2

Determine the number of jelly beans after Sophie eats 10 of each

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Answer

Sophie eats 10 jelly beans of each color, so we subtract 10 from both the red and blue jelly beans:

New count of red jelly beans: $52 - 10 = 42$
New count of blue jelly beans: $78 - 10 = 68$ .

Step 3

Calculate the new ratio of red to blue jelly beans

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Answer

Now we can find the new ratio of red to blue jelly beans, which is:

$\text{New Ratio} = \frac{\text{Red}}{\text{Blue}} = \frac{42}{68} = \frac{21}{34} = \frac{21 \div 7}{34 \div 7} = \frac{3}{4.8}$

To express this in the format of whole numbers:

Multiply both by 5 to simplify % 2:3 after Sophie eats.
So the new ratio, simplified, is 4:9.

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