Jim has eight more dimes than quarters in his pocket for a total of $2.90. the equation 0.10(x + 8) + 0.25(x) = 2.90 models the number of quarters, x, in his pocket. how many quarters are in jim's pocket?

We are given: Jim has eight more dimes than quarters.

Let us assume Jim has number of quarters = x.

Number of dimes  = number of quarters + 8 = x + 8.

Total value = $2.90.

So,  equation would be 0.10(x + 8) + 0.25(x) = 2.90 .

Let us solve equation for x now.

Distributing 0.10 over (x+8) we get

0.10x + 0.8 +  + 0.25x = 2.90

Comining like terms.

0.35x +0.8 = 2.90.

Subtracting 0.8 from both sides, we get

0.35x +0.8-0.8 = 2.90 - 0.8

0.35x = 2.1

Dividing both sides by 0.35, we get

x = 6.

Therefore, 6 quarters are in jim's pocket.

table 3 represents a direct variation function. : )

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .