Question

How many ways can you make change for 60¢ using only nickels, dimes, and quarters?

Answer 1

You can make 60cents using nickels dimes and quarters about 10 or more times

Answer 2

There are 13 ways to make change for 60¢ using only nickels, dimes and quarters.

Determination of the number of combinations for a given amount of money

In the United States of America, a nickel equals 0.05 dollar, a dime equals 0.10 dollar and a quarter equals 0.25 dollar.  

For 0.60 dollar we have the following expression in terms of nickels ($n$), dimes ($d$) and quarters ($q$):

$0.25\cdot q + 0.10\cdot d + 0.05\cdot n = 0.60$, where $q,\,d,\,n \in \mathbb{N}_{O}$ (1)

Since quarters are the money of greatest value, we assume arbitrary quantities and count corresponding solutions, whose representations are included below:

Case 1 ($q = 0$)

$n = 12-2\cdot d$ (2)

According to the first graph, there are seven forms in this scenario.

Case 2 ($q = 1$)

$n = 7-2\cdot d$ (3)

According to the graph case_2, there are four forms in this scenario.

Case 3 ($q = 2$)

$n = 2- 2\cdot d$

According to the graph case_3, there are two forms in this scenario.

Hence, there are 13 forms to make change for 60¢ using only nickels, dimes and quarters. $\blacksquare$

To learn more on combinations, we kindly invite to check this verified question: https://brainly.com/question/1216161