You go to a convenience store to buy candy and find the...

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 $636.3 \mathrm{~g}$ of pennies, and each penny weighs $3.03 \mathrm{~g}$. Each dime weighs $2.29 \mathrm{~g}$. Each piece of candy weighs $10.23 \mathrm{~g}$. 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?

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 $636.3 \mathrm{~g}$ of pennies, and each penny weighs $3.03 \mathrm{~g}$. Each dime weighs $2.29 \mathrm{~g}$. Each piece of candy weighs $10.23 \mathrm{~g}$.
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?

Key Concepts

Unit Conversion

This concept involves converting between different units, such as using the total weight in grams and the weight of an individual item (coin or candy) to calculate a total count. For example, dividing the total weight of coins by the weight of one coin allows you to determine how many coins you have, and similarly for candy.

Division and Rounding

Often real?world quantities require the use of division that may result in non?integer quotients. In such cases, it is important to round appropriately (usually rounding down) since you can only have whole items like coins or pieces of candy. This concept ensures that the computed counts make sense in a physical context.

Multiples and Divisibility Constraints

Some problems impose restrictions on how quantities can be grouped or purchased. Here, candy is sold only in specific multiples (such as multiples of four), which requires understanding of factors and divisibility. Recognizing these constraints is essential for valid problem solving under such conditions.

Proportional Reasoning

This involves understanding relationships between quantities that change in proportion to each other. In the context of coin denominations and candy pricing, proportional reasoning helps connect the number of coins, their total monetary value, and the number of candies that can be purchased, ensuring the ratios remain consistent.

Optimal Resource Allocation

This concept is about making the best use of limited resources to reach a desired outcome—in this case, purchasing as much candy as possible given the constraints of coin denominations and available weight. It requires balancing the available resources (coins) against the cost requirements for each candy purchase.

Linear Scaling

Linear scaling describes how increases in one quantity lead to proportional increases in another. For instance, when the number of coins is doubled, the potential number of candy purchases also doubles, assuming all other factors remain constant. This concept is important when determining outcomes under modified conditions, such as having twice as many coins.

Transcript

Please give Ace some feedback