Alexis has some dimes and quarters.
Her coins have a total value of $5.80
She has a total of 40 coins
Which of the following systems of equations can be used to find the number of dimes, d, and the number of quarters, q, that Alexis has?

A. d+q=5.80 40d+40q=5.80
B. d+q=40 5.80d+5.80q=40
C. d+q=5.80 0.10d+0.25q=40

The number of dimes and the number nickels Alexis has can be found by

writing equations based on the given information.

Reasons:

The given information on the coins are;

Total value of the coins = $5.80

Total number of coins = 40 coins

Denomination of the coins = Dimes, d and quarters, q

Required: The system of equation that can be used to find the number of dimes, d and the number of quarters, q, Alexis has

Solution:

The value of one Dime = $0.10

The value of a Quarter = $0.25

Therefore;

0.1 × Number of Dime + 0.25 × Number of  Quarters = 5.80

Number of Dimes + Number of Quarters = 40

Which gives;

0.1·d + 0.25·q = 5.80

d + q = 40

The correct option is therefore; d + q = 40, 0.1·d + 0.25·q = 5.80

Learn more about writing equations here:

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C. d + q = 5.80

0.10d + 0.25q = 40

Step-by-step explanation:

We are given a situation where Alexis has some dimes and quarters, all her coins have a value of $5.80 / and have a total of 40 coins.

So lets look at the equation for 40 coins.

We are looking for how many dimes and quarters equal to $5.80 and make up 40 in total

Therefore :

We have to add dimes and quarters together to make up $5.80 dollars

d + q = 5.80

This makes B. Incorrect because it has d + q = 40 instead of d + q = 5.80

Now for the amount of coins in total.

We have to find the amount of each coin costs. So a quarter is 25 cents, and a dime is 10 cents. So we add those together to make up 40 coins in total.

0.10d + 0.25q = 40

A. becomes incorrect because is has 40d + 40q = 5.80, which already goes over the amount asked and does not have the correct system of equation.

Therefore leaving you with C.

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