Answer:
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
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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
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5 + 8 + 4 = 17
17 = 17
