Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

A boutique in Allenville specializes in leather goods for men. Last month, the company sold 93 wallets and 44 belts, for a total of $4,945. This month, they sold 62 wallets and 95 belts, for a total of $7,762. How much does the boutique charge for each item?

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absor201 absor201 · Answer 1 · 2020-02-08T17:06:33+01:00

One wallet costs $21 and one belt costs $68.

Step-by-step explanation:

Let,

x represent the cost of each wallet

y represent the cost of each belt

According to given statement;

93x+44y=4945 Eqn 1

62x+95y=7762 Eqn 2

Multiplying Eqn 1 by 62

[tex]62(93x+44y=4945)\\5766x+2728y=306590\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 93

[tex]93(62x+95y=7762)\\5766x+8835y=721866\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 3 from Eqn 4

[tex](5766x+8835y)-(5766x+2728y)=721866-306590\\5766x+8835y-5766x-2728y=415276\\6107y=4415276[/tex]

Dividing both sides by 6107

[tex]\frac{6107y}{6107}=\frac{415276}{6107}\\\\y=68[/tex]

Putting y=68 in Eqn 1

[tex]93x+44(68)=4945\\93x+2992=4945\\93x=4945-2992\\93x=1953[/tex]

Dividing both sides by 93

[tex]\frac{93x}{93}=\frac{1953}{93}\\x=21[/tex]

One wallet costs $21 and one belt costs $68.

Keywords: linear equation, elimination method

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