Solve the equation modeled by the envelopes and counters by moving the correct number of counters to each envelope. Then, enter the numeric solution to the equation.

a) Envelope 1: 8 counters, Envelope 2: 5 counters
b) Envelope 1: 6 counters, Envelope 2: 7 counters
c) Envelope 1: 9 counters, Envelope 2: 4 counters
d) Envelope 1: 3 counters, Envelope 2: 10 counters

Question

20-10-2023
Mathematics

High School

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Solve the equation modeled by the envelopes and counters by moving the correct number of counters to each envelope. Then, enter the numeric solution to the equation.

a) Envelope 1: 8 counters, Envelope 2: 5 counters
b) Envelope 1: 6 counters, Envelope 2: 7 counters
c) Envelope 1: 9 counters, Envelope 2: 4 counters
d) Envelope 1: 3 counters, Envelope 2: 10 counters

Answer :

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muhammadqadeer4187 muhammadqadeer4187 · Answer 1 · 2023-07-17T21:34:23-04:00

Final Answer:

The solution to the equation is: Envelope 1: 8 counters, Envelope 2: 5 counters,So,the correct option is a.

Explanation:

To find the solution to the equation modeled by the envelopes and counters, we need to balance the number of counters in each envelope. In this case, for option (a), moving 3 counters from Envelope 1 to Envelope 2 will result in both envelopes having an equal number of counters, with 5 counters in each. Therefore, the solution to the equation is Envelope 1: 8 counters, Envelope 2: 5 counters.

This solution is obtained by subtracting the excess counters in Envelope 1 (8 counters) by the difference in the counters between the two envelopes (3 counters). Mathematically, this can be represented as 8 - 3 = 5. The goal is to achieve a balance, ensuring that the number of counters in each envelope is equal. Thus, by moving 3 counters from Envelope 1 to Envelope 2, we reach the solution presented in the final answer.

In summary, the solution to the equation is determined by adjusting the counters between the envelopes to achieve an equal distribution, and in this case, it is Envelope 1: 8 counters, Envelope 2: 5 counters,Thus, the correct option is a.