She is charging $12 for large prints and $9 for small prints.
Step-by-step explanation:
Let,
Large prints = x
Small prints = y
According to given statement;
10x+3y=147 Eqn 1
6x+4y=108 Eqn 2
Multiplying Eqn 1 by 4;
[tex]4(10x+3y=147)\\40x+12y=588\ \ \ \ Eqn\ 3[/tex]
Multiplying Eqn 2 by 3;
[tex]3(6x+4y=108)\\18x+12y=324\ \ \ \ Eqn\ 4[/tex]
Subtracting Eqn 4 from Eqn 3;
[tex](40x+12y)-(18x+12y)=588-324\\40x+12y-18x-12y=264\\22x=264[/tex]
Dividing both sides by 22,
[tex]\frac{22x}{22}=\frac{264}{22}\\x=12[/tex]
Putting x=12 in Eqn 1;
[tex]10(12)+3y=147\\120+3y=147\\3y=147-120\\3y=27\\[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{27}{3}\\y=9[/tex]
She is charging $12 for large prints and $9 for small prints.
Keywords: linear equation, subtraction
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