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.

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