Question

Bella wants to create a tea-mix. She can buy Asian Treasure tea for $7.50 per ounce and Paradise tea for $5.00 per ounce. If she wants to make 60 ounces of tea-mix at a cost of $6.00 per ounce, how many ounces of Asian Treasure tea and how many ounces of Paradise tea should she buy?

Answer 1

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Answer:

• 24 oz Asian Treasure
• 36 oz Paradise

Explanation:

The proportion of Asian Treasure is the difference in price of the mix and Paradise tea, divided by the difference in price of Asian Treasure and Paradise tea. So the amount of Asian Treasure is ...

(6.00 -5.00)/(7.50 -5.00)(60 ounces) = 24 ounces . . . Asian Treasure tea

The remaining 60-24 = 36 ounces will be Paradise tea.

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Using an equation

You can get the same result if you define a variable (a) to the amount in ounces of the higher-priced contributor. Then the lower-priced contributor will be in the amount (60-a) ounces. The total cost of the mix is ...

7.50a +5.00(60 -a) = 60(6.00)

(7.50 -5.00)a +60(5.00) = 60(6.00) . . . rearrange the left side

(7.50 -5.00)a = 60(6.00 - 5.00) . . . . . . subtract 60(5.00)

a = 60(6.00 -5.00)/(7.50 -5.00) . . . . . . divide by the coefficient of 'a'

Note that this last expression is identical to the one we used above to find the quantity of Asian Treasure tea.