Kevin and randy muise have a jar containing 69 coins, all of which are either quarters or nickels. the total value of the coins in the jar is $nbsp 9.05. how many of each type of coin do they have?

Let us assume number of quarters = q.

Let us assume number of nickels = n.

Total number of coins = 69.

We can setup first eqation,

Number of quarters + number of nickels = 69.

q + n = 69 equation(1).

Total value of all the coins = $9.05

We can setup second equation as,

0.25*number of quarters + 0.05*number of nickels  - $9.05.

0.25q + 0.05n =9.05   equation(2).

We got two equations of a system of equation.

Let us apply substitution mehod of solving system of linear equations.

Solving first equation q+n=69 for n.

Adding q on both sides of the equation, we get

q-q+n = 69-q.

n= 69-q.

We need substitute n=69-q in second equation 0.25q + 0.05n =9.05.

0.25q +0.05(69-q) = 9.05

Distributing 0.05 over (69-q).

0.25q +0.05*69 -0.05*q =9.05.

0.25q +3.45 -0.05q =9.05

Combining like terms 0.025q -0.05q, we get

0.20q +3.45 =9.05

Subtracting 3.45 from both sides.

0.20q +3.45-3.45 =9.05-3.45

0.20q = 5.6

Dividing both sides by 0.20

0.20q/0.20 = 5.6/0.20

q = 28.

Plugging q=28 in equation(1)

q+n =69    => 28 +n =69

Subtracting 28 from both sides, we get

28-28 +n =69-28.

n = 41.

Therefore, number of quarters 28 and number of nickels 41.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

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