We have discussed three representation of proportionality. If x is proportional

Question

We have discussed three representation of proportionality. If x is proportional to y, then Scaling If you scale one quantity by a number, you scale the other quantity by the same number (x . a rightarrow y . a) Constant Ratio: the ratio of the two quantities is constant. That is y/a = m where we calI m the constant of proportionality Constant Multiple: one quantity is a constant multiple of the other That it y = mx. When making lemonade using a powdered mix, the recipe suggests a mixture of 20 cups of water for every 8 scoops of mix. Suppose you want to use 12 scoops of powdered mix. How much water do you need? Explain how you are thinking about this problem to come up with your answer Solve the problem given using each of the three ways of thinking proportionally described above Include any diagrams or illustrations as necessary. The grocery store sells turkey at their deli with the cost of the purchase based on the number of pounds of turkey a customer purchases. A customer is charged $1.86 for 0.2 pounds of turkey. Assume that the deli charges a fixed cost per pound of turkey sold. How much money will a customer be charged if she purchase 0.8 pounds of turkey? 1.4 pounds of turkey? Explain your reasoning. How many pounds of turkey can a customer purchase for $1 5?

Explanation / Answer

1) Number of cups used will be directly proportional to the mix used

Using the second law, number of cups/mix should be constant

number of cups(1)/mix(1) = number of cups(2)/mix(2)

20/8 = number of cups(2)/12

number of cups(2) = 20 * 12/8 = 30 cups

Hence the water needed is equal to 30 cups

2)

Using the second law again,

price of turkey/amount of turkey will be a constant

For 0.8 pounds of turkey

1.86/0.2 = Price/0.8

Price = $1.86 * 4 = $7.44

For 1.4 pounds of turkey

1.86/0.2 = Price/1.4

Price = $1.86 * 7 = $13.02

b)

using the same formula

1.86/0.2 = 15/amount of turkey

amount of turkey = 15 * 0.2/1.86 = 1.6129 pounds of turkey

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