In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?

5 ball pens

Explanation:

Let's first assign our variables:

x = number of ball pens    = 0.05 each

y = number of gel pens    = 0.10 each

z = number of ink pens    = 0.25 each

We have three equations there:

She bought 17 pens so this means that if we add all the number of pens together we get 17.

The total cost is $2.05, so if we add the cost of the all the pens we would get $2.05.

Lastly, we know that she bought twice as many gel pens as ink pens.

We can then assume:

x + y + z = 17

0.05x + 0.10y + 0.25 z = 2.05

y = 2z

we will need to use all of these to figure out the number of ball pens:

x + y + z = 17

Substitute the equation we came up for y (y = 2z):

x + 2z + z = 17

x + 3z = 17

x = 17 - 3z

0.05x + 0.10y + 0.25 z = 2.05

0.05x + 0.10(2z) + 0.25z = 2.05

0.05(17-3z) + 0.20z + 0.25z = 2.05

0.85 - 0.15z + 0.20z + 0.25z = 2.05

Combine like terms:

0.85 + 0.3z = 2.05

Subtract both sides by 0.85

0.85 + 0.3z - 0.85 = 2.05 - 0.85

0.3z = 1.2

Divide both sides by 0.3

0.3z/0.3 = 1.2/0.3

z = 4

Now that we have the number of ink pens, let's solve the number of ball pens using one of the formulas we came up with.

x = 17 - 3z

x = 17 - 3(4)

x = 17 - 12

x = 5

If you want to check, just plug in everything that we know.

y = 2x

y = 2(4)

y = 8

5 + 8 + 4 = 17

17 = 17

(a) when insurance is obtained through a reciprocal insurer, the insureds are sharing the risk of loss with other subscribers of that reciprocal.

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