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Sagot :
Let's work through both parts of the question step-by-step.
### Part 1: Number of Pink Counters
We are given that there are 180 counters in total, and they are either blue, yellow, or pink. We know the fractions of blue and yellow counters:
1. Number of blue counters:
[tex]\[ \frac{3}{5} \text{ of the counters are blue}. \][/tex]
Calculating the number of blue counters:
[tex]\[ \text{Number of blue counters} = \frac{3}{5} \times 180 = \frac{3 \times 180}{5} = 3 \times 36 = 108 \][/tex]
2. Number of yellow counters:
[tex]\[ \frac{1}{4} \text{ of the counters are yellow}. \][/tex]
Calculating the number of yellow counters:
[tex]\[ \text{Number of yellow counters} = \frac{1}{4} \times 180 = \frac{180}{4} = 45 \][/tex]
3. Number of pink counters:
[tex]\[ \text{Total counters} - \text{Number of blue counters} - \text{Number of yellow counters} \][/tex]
[tex]\[ \text{Number of pink counters} = 180 - 108 - 45 = 27 \][/tex]
So, the number of pink counters is 27.
### Part 2: Julie's Total Profit
Julie buys 180 flowers for £60 and sells them at different prices. We need to calculate the total revenue and then the profit.
1. Number of flowers sold at £2 each:
[tex]\[ \text{A quarter of the flowers are sold at } £2 \text{ each}. \][/tex]
Calculating the number of flowers sold at £2 each:
[tex]\[ \text{Number of flowers sold at £2} = \frac{1}{4} \times 180 = 45 \][/tex]
2. Number of flowers sold at £3 each:
[tex]\[ \text{A third of the flowers are sold at } £3 \text{ each}. \][/tex]
Calculating the number of flowers sold at £3 each:
[tex]\[ \text{Number of flowers sold at £3} = \frac{1}{3} \times 180 = 60 \][/tex]
3. Number of flowers sold at £1 each:
The remaining flowers are sold at £1 each.
[tex]\[ \text{Number of remaining flowers} = 180 - 45 - 60 = 75 \][/tex]
4. Calculating the total revenue:
- Revenue from flowers sold at £2 each:
[tex]\[ \text{Revenue} = 45 \times 2 = 90 \][/tex]
- Revenue from flowers sold at £3 each:
[tex]\[ \text{Revenue} = 60 \times 3 = 180 \][/tex]
- Revenue from flowers sold at £1 each:
[tex]\[ \text{Revenue} = 75 \times 1 = 75 \][/tex]
Adding all these revenues together, we get the total revenue:
[tex]\[ \text{Total revenue} = 90 + 180 + 75 = 345 \][/tex]
5. Calculating the total profit:
[tex]\[ \text{Profit} = \text{Total revenue} - \text{Total cost} \][/tex]
[tex]\[ \text{Profit} = 345 - 60 = 285 \][/tex]
Therefore, Julie's total profit is £285.
### Part 1: Number of Pink Counters
We are given that there are 180 counters in total, and they are either blue, yellow, or pink. We know the fractions of blue and yellow counters:
1. Number of blue counters:
[tex]\[ \frac{3}{5} \text{ of the counters are blue}. \][/tex]
Calculating the number of blue counters:
[tex]\[ \text{Number of blue counters} = \frac{3}{5} \times 180 = \frac{3 \times 180}{5} = 3 \times 36 = 108 \][/tex]
2. Number of yellow counters:
[tex]\[ \frac{1}{4} \text{ of the counters are yellow}. \][/tex]
Calculating the number of yellow counters:
[tex]\[ \text{Number of yellow counters} = \frac{1}{4} \times 180 = \frac{180}{4} = 45 \][/tex]
3. Number of pink counters:
[tex]\[ \text{Total counters} - \text{Number of blue counters} - \text{Number of yellow counters} \][/tex]
[tex]\[ \text{Number of pink counters} = 180 - 108 - 45 = 27 \][/tex]
So, the number of pink counters is 27.
### Part 2: Julie's Total Profit
Julie buys 180 flowers for £60 and sells them at different prices. We need to calculate the total revenue and then the profit.
1. Number of flowers sold at £2 each:
[tex]\[ \text{A quarter of the flowers are sold at } £2 \text{ each}. \][/tex]
Calculating the number of flowers sold at £2 each:
[tex]\[ \text{Number of flowers sold at £2} = \frac{1}{4} \times 180 = 45 \][/tex]
2. Number of flowers sold at £3 each:
[tex]\[ \text{A third of the flowers are sold at } £3 \text{ each}. \][/tex]
Calculating the number of flowers sold at £3 each:
[tex]\[ \text{Number of flowers sold at £3} = \frac{1}{3} \times 180 = 60 \][/tex]
3. Number of flowers sold at £1 each:
The remaining flowers are sold at £1 each.
[tex]\[ \text{Number of remaining flowers} = 180 - 45 - 60 = 75 \][/tex]
4. Calculating the total revenue:
- Revenue from flowers sold at £2 each:
[tex]\[ \text{Revenue} = 45 \times 2 = 90 \][/tex]
- Revenue from flowers sold at £3 each:
[tex]\[ \text{Revenue} = 60 \times 3 = 180 \][/tex]
- Revenue from flowers sold at £1 each:
[tex]\[ \text{Revenue} = 75 \times 1 = 75 \][/tex]
Adding all these revenues together, we get the total revenue:
[tex]\[ \text{Total revenue} = 90 + 180 + 75 = 345 \][/tex]
5. Calculating the total profit:
[tex]\[ \text{Profit} = \text{Total revenue} - \text{Total cost} \][/tex]
[tex]\[ \text{Profit} = 345 - 60 = 285 \][/tex]
Therefore, Julie's total profit is £285.
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