Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters. They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding. Solve this problem for Jack.

Question

Jayden

Mathematics

28 May, 09:28

Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters. They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding. Solve this problem for Jack.

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Answers (1)

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Puffy · Answer 1

Lulu has 14 quarters and 6 dimes

Step-by-step explanation:

Let x be the number of dimes and y the number of quarters. The sum of quarters and dime is 20 coins. Then:

x + y = 20

We also know that the value of each dime is $ 0.10 and the value of each quarter is $0.25. The total value of the coins is $4.10. Then, the number of dimes times 0.10 plus the number of quarters times 0.25 will be 4.10:

0.10x + 0.25y = 4.10

So, we have a system of 2 equations and 2 unknowns:

x + y = 20

0.10x + 0.25y = 4.10

Let's solve the first equation for y:

x + y = 20

subtract x from both sides

y = 20 - x

And now let's replace y in the second equation:

0.10x + 0.25 (20 - x) = 4.10

Apply distributive property

0.10x + 5 - 0.25x = 4.10

subtract 5 from both sides of the equation

-0.15x = - 0.9

Divide by - 0.15 both sides of the equation

x = 6

Now let's calculate y:

y = 20 - x

y = 20 - 6 = 14

Lulu has 14 quarters and 6 dimes