The cost of one pack of pencils is $1.50 and cost of one pack of pens is $1.75
Step-by-step explanation:
We can create a system of equations from the given information and then solve it for the value of x and y.
Let,
x be the cost of one pack of pencils
y be the cost of one pack of pens
According to given statement;
2x+3y=8.25 Eqn 1
5x+2y=11.00 Eqn 2
Multiplying Eqn 1 by 2;
[tex]2(2x+3y=8.25)\\4x+6y=16.5\ \ \ Eqn\ 3[/tex]
Multiplying Eqb 2 by 3;
[tex]3(5x+2y=11.00)\\15x+6y=33.00\ \ \ Eqn\ 4[/tex]
Subtracting Eqn 3 from Eqn 4
[tex](15x+6y)-(4x+6y)=33.00-16.5\\15x+6y-4x-6y=16.50\\11x=16.50\\[/tex]
Dividing both sides by 11
[tex]\frac{11x}{11}=\frac{16.50}{11}\\x=1.50[/tex]
Putting x=1.5 in Eqn 1
[tex]2(1.50)+3y=8.25\\3.00+3y=8.25\\3y=8.25-3.00\\3y=5.25[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{5.25}{3}\\y=1.75[/tex]
The cost of one pack of pencils is $1.50 and cost of one pack of pens is $1.75
Keywords: linear equation, elimination method
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