Question

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Explanation:

Find the greatest common divisor of the coin counts

The problem asks us to distribute 75 nickels, 45 dimes, and 120 quarters equally among Grandma Anne's grandchildren. To find the maximum number of grandchildren she can distribute these coins to equally, we need to find the Greatest Common Divisor (GCD) of the three quantities: 75, 45, and 120.

Using the Word Problems knowledge point, we find the prime factorizations:

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The common prime factors are 3 and 5. Thus, the greatest common divisor is:

$$ \text{GCD}(75, 45, 120) = 3 \times 5 = 15 $$

So, she could give coins to 15 grandchildren.

Calculate the number of each coin per grandchild

Now, we divide each coin total by the number of grandchildren (15) to find how many of each coin type each grandchild receives:

• Nickels:

$$ \frac{75}{15} = 5 $$

• Dimes:

$$ \frac{45}{15} = 3 $$

• Quarters:

$$ \frac{120}{15} = 8 $$

Each grandchild receives 5 nickels, 3 dimes, and 8 quarters.

Answer:

Grandma Anne has coins that she wants to distribute equally to her grandchildren. If she has 75 nickels, 45 dimes, and 120 quarters, she could give coins to <blank>15</blank> grandchildren. Each grandchild would receive <blank>5</blank> nickels, <blank>3</blank> dimes, and <blank>8</blank> quarters.