Question

On a timed session please help I have one more question after this.....
Felipe's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Felipe 5.25 per pound, and type B coffee costs 4.10 per pound. This month, Felipe made 142 pounds of the blend, for a total cost of 642.00 . How many pounds of type A coffee did he use?

Answer 1

Felipe used 52 pounds of Type A coffee.

Step-by-step explanation:

Cost of Type A coffee = 5.25 per pound

Cost of Type B coffee = 4.10 per pound

Coffee blended this month = 142 pounds

Total cost of 142 pounds = 642.00

Let,

x be the pounds of Type A coffee

y be the pounds of Type B coffee

According to given statement;

x+y=142        Eqn 1

5.25x+4.10y=642    Eqn 2

Multiplying Eqn 1 by 4.10

$4.10(x+y=142)\\4.10x+4.10y=582.20\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(5.25x+4.10y)-(4.10x+4.10y)=642-582.20\\5.25x+4.10y-4.10x-4.10y=59.80\\1.15x=59.80$

Dividing both sides by 1.15

$\frac{1.15x}{1.15}=\frac{59.80}{1.15}\\x=52$

Felipe used 52 pounds of Type A coffee.

Keywords: linear equation, elimination method

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