Question

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.

Answer 1

Lulu has 14 quarters and 6 dimes

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