Question

Stephanie has 20 coins in her purse.

• Some are quarters.
• Some are dimes.
• The total value of the coins is $3.35.
How many of each type of coin does she have?

Answer 1

To solve this problem, set up a system of equations using x for quarters and y for dimes. Solve for x and substitute it back into one of the equations to find y.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's let x represent the number of quarters and y represent the number of dimes. We know that the total number of coins is 20, so we have one equation: x + y = 20. We also know that the total value of the coins is $3.35, so we have another equation: 0.25x + 0.10y = 3.35. Now we can solve this system of equations.

We can start by multiplying the first equation by 0.10 to get the second equation in terms of y: 0.10x + 0.10y = 2. We can subtract this equation from the second equation we already have to eliminate y: 0.25x + 0.10y - (0.10x + 0.10y) = 3.35 - 2. Simplifying the equation gives us: 0.15x = 1.35. Dividing both sides by 0.15 gives us: x = 9.

Now we can substitute the value of x into the first equation to find y: 9 + y = 20. Subtracting 9 from both sides gives us: y = 11. Therefore, Stephanie has 9 quarters and 11 dimes.

Answer 2

11 dimes and 9 quarters

Step-by-step explanation:

lets make x quarters and y dimes

Here is the equation we have so far:

x+y=20

BUT it can also be used to determine the values:

0.25x+0.10y=3.35

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0.25x+0.10y=3.35

x+y=20

Im going to solve for quarters first.

Multiply everything by 0.25 on the bottom equation: 0.25x+0.25y=5

Now you have two equations:

0.25x+0.10y=3.35

and 0.25x+0.25y=5

subtract out the 0.25x

.15y=1.65

y=11

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you have 11 dimes.

x+11=20

x=9

You have 9 quarters