Nuts.com sells raw almonds for $10 per pound and roasted pistachios for $12 per pound. Christopher spends $70, before taxes and shipping, to purchase 6.3 total pounds of nuts. How many pounds of almonds did Christopher purchase?

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absor201 absor201 · Answer 1 · 2019-12-11T13:53:43+01:00

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.

Step-by-step explanation:

Cost of almonds per pound = $10

Cost of roasted pistachios = $12

Total amount spent = $70

Weight of nuts = 6.3

Let,

Weight of almonds = x

Weight of roasted pistachios = y

According to given statement;

x+y=6.3 Eqn 1

10x+12y=70 Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=6.3)\\10+10y=63\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2;

[tex](10x+12y)-(10x+10y)=70-63\\10x+12y-10x-10y=7\\2y=7[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{7}{2}\\y=3.5[/tex]

Putting y=3.5 in Eqn 1

[tex]x+3.5=6.3\\x=6.3-3.5\\x=2.8[/tex]

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.

Keywords: linear equations, elimination method

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