You go to a convenience store to buy candy and find the owner to be rather odd. He allows you to buy pieces in multiples of four, and to buy four, you need $0.23. He only allows you to do this by using 3 pennies and 2 dimes. You have a bunch of pennies and dimes, and instead of counting them, you decide to weigh them. You have 636.3 g of pennies, and each penny weighs 3.03 g. Each dime weighs 2.29 g. Each piece of candy weighs 10.23 g. a. How many pennies do you have? b. How many dimes do you need to buy as much candy as possible? c. How much should all these dimes weigh? d. How many pieces of candy could you buy? (number of dimes from part b) e. How much would this candy weigh? f. How many pieces of candy could you buy with twice as many dimes?

Step by step solution

01

Find the number of pennies

To find how many pennies the student has, we need to divide the total weight of pennies by the weight of a single penny: Number of pennies = Total weight of pennies / Weight of a single penny Number of pennies = \( \frac{636.3}{3.03} \)

02

Calculate how many pieces of candy can be bought

Find out how many sets of four pieces of candy the student can buy using the number of pennies found in Step 1. Since each set of four candy costs 3 pennies ($0.03), divide the number of pennies by 3 to find how many sets of four can be bought: Number of sets of four pieces of candy = Number of pennies / 3

03

Find the number of dimes needed

Since the student can buy sets of four candy using 2 dimes each, multiply the number of sets found in step 2 by 2 to find the number of dimes required: Number of dimes needed = Number of sets of four pieces of candy × 2

04

Calculate the total weight of the dimes

Multiply the number of dimes needed from Step 3 by the weight of a single dime to find the total weight of the dimes: Total weight of dimes = Number of dimes needed × Weight of a single dime

05

Find the total weight of the candy bought

Multiply the number of sets of candy found in Step 2 with the weight of each piece of candy (10.23 g). Since there are 4 pieces per set of candy, multiply by 4 too: Total weight of candy = Number of sets of four pieces of candy × Weight of a single candy × 4

06

Calculate how many pieces of candy can be bought with twice as many dimes

First, Find the new number of sets of four pieces of candy that can be bought with twice as many dimes: New number of sets of four pieces of candy = (Number of dimes needed × 2) / 2 Next, calculate total pieces of candy by multiplying the new number of sets by 4 (pieces per set): Total pieces of candy bought with twice as many dimes = New number of sets of four pieces of candy × 4

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