Section A has two items. Item 1 is about a spice vendor. Item 2 is about data plans and cake baking. Both items have tasks.

Mathematics
Section A has two items. Item 1 is about a spice vendor. Item 2 is about data plans and cake baking. Both items have tasks.

ScanSolve AI Answer

Here's the solution for Item 1:

Item 1

(a) Will the first client be able to get his order with the amount of C he wants?

Step 1: Determine the proportion of ingredient C in the original mixture. The original mixture consists of 2 cups of A, 3 cups of B, and 5 cups of C. Total cups in the mixture = 2+3+5=102 + 3 + 5 = 10 cups. The proportion of ingredient C in the original mixture is: Cups of CTotal cups=510=0.5\frac{\text{Cups of C}}{\text{Total cups}} = \frac{5}{10} = 0.5

Step 2: Compare the proportion of C in the original mixture with the client's requirement. The client wants the measure of ingredient C to be 0.6. Since 0.5≠0.60.5 \neq 0.6, the original mixture does not meet the client's requirement.

Answer: No, the first client will not be able to get his order with the amount of C he wants, as the original mixture has a proportion of 0.5 for ingredient C, while the client requires 0.6.

(b) Determine the number of cups of B that will be needed for the 9 kg the second client has asked for.

Step 1: Determine the total number of cups required for 9 kg of spice. The original mixture of 10 cups yields 1.5 kg of spice. To find the number of cups per kg: Cups per kg=10 cups1.5 kg=1032=203 cups/kg\text{Cups per kg} = \frac{10 \text{ cups}}{1.5 \text{ kg}} = \frac{10}{\frac{3}{2}} = \frac{20}{3} \text{ cups/kg} For 9 kg of spice, the total cups needed are: Total cups for 9 kg=203 cups/kg×9 kg=20×3=60 cups\text{Total cups for 9 kg} = \frac{20}{3} \text{ cups/kg} \times 9 \text{ kg} = 20 \times 3 = 60 \text{ cups}

Step 2: Calculate the number of cups of B needed for 60 total cups. In the original mixture, there are 3 cups of B out of 10 total cups. The proportion of B is 310\frac{3}{10}. Number of cups of B for the 9 kg order: Cups of B=310×60 cups=3×6=18 cups\text{Cups of B} = \frac{3}{10} \times 60 \text{ cups} = 3 \times 6 = 18 \text{ cups}

Answer: The number of cups of B needed for the 9 kg order is 18 cups\boxed{\text{18 cups}}.

(c) Help the vendor to determine his new selling price for 1 kg in order to make his desired profit and the price of 9 kg that he will charge the client.

Step 1: Calculate the profit amount per kg. The cost to make 1 kg of spice is sh 4500. The desired profit is 30%. Profit per kg=30% of sh 4500=0.30×4500=sh 1350\text{Profit per kg} = 30\% \text{ of sh } 4500 = 0.30 \times 4500 = \text{sh } 1350

Step 2: Calculate the new selling price per kg. Selling price per kg=Cost per kg+Profit per kg=4500+1350=sh 5850\text{Selling price per kg} = \text{Cost per kg} + \text{Profit per kg} = 4500 + 1350 = \text{sh } 5850

Step 3: Calculate the total price for 9 kg of spice. Price of 9 kg=Selling price per kg×9 kg=5850×9=sh 52650\text{Price of 9 kg} = \text{Selling price per kg} \times 9 \text{ kg} = 5850 \times 9 = \text{sh } 52650

Answer: The new selling price for 1 kg is sh 5850\boxed{\text{sh 5850}}, and the price of 9 kg that he will charge the client is sh 52650\boxed{\text{sh 52650}}.

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