Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each kind of coin does she have?

Sagot :

Let's set up the equations we know.
Q+D=100, where Q=number of quarters, and D=number of dimes
.25Q + .1D = 21.40 (because a quarter is worth .25 and a dime worth .10)

Using the first equation, let's isolate one of our variables. I'll pick Q.
Q+D=100
Subtract D from each side
Q=100 - D

Now that we have this new equation, let's plug it into our second equation.
.25Q + .1D = 21.40
.25(100-D) + .1D = 21.40
Distribute the .25
25 - .25D + .1 D = 21.40
Combine like terms
25 - .15D = 21.40
Subtract 21.40 from each side
3.6 - .15D = 0
Add .15 D to each side
3.6 = .15D
Divide each side by .15
D = 24

Now that we have D, we can solve for Q
Q= 100 - D
= 100 - 24
Q = 76

Sue has 24 dimes and 76 quarters.

Let's check our work to make sure.
.25(76) + .1(24) = 
19 + 2.4 = 21.4 √
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.