Math help???

Question

ken has 22 coins some are which of dimes and the rest are quarters altogethor the coins are worth more than 3.40 at least how many coins are quarters? at most how many are dimes let q represent the number of quarters
thnks!

Answer 1

let

x = dimes

y = quarters

22 = total quarters

0.1x = value of dimes

0.25y = value of quarters

3.40 = total value of dimes and quarters

- - - - - - - - - - - - - - - -

x + y = 22- - - - - - - - - - - - Equation 1
0.1x + 0.25y = 3.40- - - - -Equation 2
- - - - - - - - - - - - - - -

Substitute method equation 1
x + y = 22
x + y - x = - x + 22
y = - x + 22

Substitute the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

0.1x + 0.25y = 3.40

0.1x + 0.25( - x + 22) = 3.40

0.1x + ( - 0.25x + 5.5) = 3.40

0.1x - 0.25x + 5.5 = 3.40

- 0.15x + 5.5 = 3.40

- 0.15x + 5.5 - 5.5 = 3.40 = 5.5

- 0.15x = - 2.1

- 0.15x / - 0.15 = - 2.1/ - 0.15

x = - 2.1 / - 0.15

x = 14

Insert the x value into equation 1

- - - - - - -- - - - - - - - - - - - - - - - - -

x + y = 22

14 + y = 22

14 + y - 14 = 22 - 14

y = 8

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

x + y = 22

14 + 8 = 22

22 = 22

- - - - - - - -

Check for equation 2

0.1x + 0.25y = 3.40

0.1(14) + 0.25(8) = 3.40

1.4 + 2 = 3.40

3.40 = 3.40

- - - - - - - - - - -

Both equations balance

The solution set is { 14, 8 }

There were 14 dimes and 8 quarters

- - - - - - - -s-

Answer 2

8 Quarters and 14 dimes

Answer 3

q = no of quarters
d = 22-q = no of dimes

Then 25q + 10(22-q) >= 340
15q + 220 >= 340
15q >= 120
q >= 8

Answer 4

Don't know don't care:)