Answer:
One pen is $4.25 and one pencil is $1.85.
Step-by-step explanation:
Let cost of pens be x and cost of pencils be y.
1. 4x+3y=22.55
2. 3x+2y=16.45
Sub. 1.-2.,
x+y=22.55-16.45
x=6.1-y
Sub. x=6.1-y into 1.,
y=1.85
x=4.25
Answer:
Cost of a box of pens = $4.25
Cost of a box of pencils = $1.85
Step-by-step explanation:
Given information:
Define the variables:
Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad 4x + 3y = 22.55[/tex]
[tex]\textsf{Equation 2}: \quad 3x + 2y = 16.45[/tex]
Multiply Equation 1 by 3:
[tex]\implies 3 \cdot 4x + 3 \cdot 3y = 3 \cdot 22.55[/tex]
[tex]\implies 12x + 9y = 67.65[/tex]
Multiply Equation 2 by 4:
[tex]\implies 4 \cdot 3x + 4 \cdot 2y = 4 \cdot 16.45[/tex]
[tex]\implies 12x + 8y = 65.80[/tex]
Subtract the equations to eliminate the term in x:
[tex]\begin{array}{r rr}& 12x+9y = &67.65\\- & 12x+8y = &65.80\\\cline{2-3} & y = & 1.85\end{array}[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 3x + 2y = 16.45[/tex]
[tex]\implies 3x + 2(1.85) = 16.45[/tex]
[tex]\implies 3x + 3.7 = 16.45[/tex]
[tex]\implies 3x =12.75[/tex]
[tex]\implies x=4.25[/tex]
Solution
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