The price of one hat is $2 and price of one pair of mittens is $5.
Step-by-step explanation:
Let,
Price of one hat = x
Price of one pair of mittens = y
According to given statement;
5x+4y=30 Eqn 1
2x+3y=19 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(5x+4y=30)\\10x+8y=60\ \ \ \ Eqn\ 3[/tex]
Multiplying Eqn 2 by 5
[tex]5(2x+3y=19)\\10x+15y=95\ \ \ \ Eqn\ 4[/tex]
Subtracting Eqn 3 from Eqn 4
[tex](10x+15y)-(10x+8y)=95-60\\10x+15y-10x-8y=35\\7y=35\\[/tex]
Dividing both sides by 7
[tex]\frac{7y}{7}=\frac{35}{7}\\y=5[/tex]
Putting y=5 in Eqn 1
[tex]5x+4(5)=30\\5x+20=30\\5x=30-20\\5x=10[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{10}{2}\\x=2[/tex]
The price of one hat is $2 and price of one pair of mittens is $5.
Keywords: linear equation, subtraction
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