Question

Systems of Equations

1. Paco's Tacos sold 280 food items from its mobile unit. Only Tacos ($2 each) and burritos ($3 each) were available. It took in $660 in sales. How many tacos and how many burritos did it sell?

2. Penelope Printing Press promptly sold 5 cent pencils and 10 cent pens to the public. It sold 1000 writing utensils and took in $74.50 in sales. How many pens and how many pencils did they sell?

Answer 1

1. t+b=280
2t+3b=660
b=-t+280
2t-3t+840=660
-t=-180
t=180
b=100
He sold 180 tacos and 100 burritos
2. x=5 cent pencils
y=10 cent pens
x+y=1000
.05x+.1y=74.5
y=-x+1000
.05x-.1x+100=74.5
-1.5x=-25.5
15x=255
x=17
y=983
They sold 17 pencils and 983 pens

Answer 2

let number of tacos be x and the burritos be y

x+y =280
2x + 3y = 660

Multiplying the first equation by 2 2x+ 2y= 560
Subtract the second equation from 1 2x +3y =660

-y=-100 y=100 so x =180 so he sold 180 tacos and 100 burritos