Answer :
Final answer:
To find the number of marbles needed to get C checkers, we establish a ratio of marbles to checkers by multiplying the number of marbles by the number of jacks and dividing by the number of checkers that j jacks can get. Then, we multiply this ratio by the number of desired checkers, yielding (m*j*C)/c.
Explanation:
Given that m marbles can be traded for J jacks, and j jacks can be traded for c checkers, we can establish a ratio to find out the number of marbles needed to get C checkers.
First, find out how many marbles make one checker by multiplying m by j (since m marbles are equivalent to J jacks and J jacks are equivalent to c checkers, so m*j/c marbles make one checker). Hence, to get C checkers, we multiply our ratio (m*j/c) by C.
So, the result will be (m*j*C)/c. This is the number of marbles needed to get C checkers.
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Final answer:
From the given ratios, the number of marbles required to trade for C checkers can be found by multiplying the rate of marbles per jack by the number of checkers and the conversion rate from jacks to checkers (mcC/J).
Explanation:
The number of marbles needed to get C checkers based on the boys' trading agreement is a question of ratios and proportions. To find this, we are essentially trying to find the equivalent number of marbles required for one checker. As given, m marbles are equivalent to J jacks and j jacks are equivalent to c checkers. Therefore, mc/J jacks would be equivalent to one checker. Since C denotes an unknown quantity of checkers, you multiply the equivalent marbles per single checker (mc/J) by C.
So, you would require mcC/J marbles to get C checkers.
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