Jon's coin collection consists of quarters, dimes and nickels. If the ratio of quarters to dimes is 5:2, and the ratio of dimes to nickels is 3:4,what is the ratio of quarters to nickels?

The ratio of quarters to nickels is:

Step-by-step explanation:

To solve the exercise, you must first consider how big is the ratio of each one to the other, when it is mentioned that the ratio of quarters to dimes is 5:2 it means that for every 5 quarters, Jon has 2 dimes, for the more quarters there are with respect to the dimes, we simply divide the larger value by the smaller:

Thus, we know that there are 2.5 more quarters than dimes. Now the following proportion: the ratio of dimes to nickels is 3:4, which means that for every 3 dimes there are 4 nickels, as the nickels are greater in quantity, we are going to see how many times they are greater in proportion than the dimes making again a division of the major over the minor:

As we can see, the nickels are a little more than 1 with respect to the dimes, now we are going to create two formulas with those values:

Where:

As you see. We only express the calculated proportions, at first glance you can identify that the number of quarters is greater, but to know how much greater with respect to nickels we are going to divide the two values ​​that accompany "d" in the formulas:

If we express it in ratio as it is in the exercise, we obtain:

So, 15:8 is the ratio of quarters to nickels, which means that for every 15 quarters, jon has 8 nickels.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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