Respuesta :
Given:
Jan buys 1 beef taco and 2 fruit cups for $5.25.
Richard buys 3 beef tacos and 1 fruit cup for $8.25.
Required:
We need to find the price of each item beef taco and fruit cup.
Explanation:
Let x be the price of a beef taco.
Let y be the price of a fruit cup.
The cost of 1 beef taco and 2 fruit cups = $ 5.25
[tex]x+2y=5.25[/tex]Subtract 2y from both sides of the equation.
[tex]x+2y-2y=5.25-2y[/tex][tex]x=5.25-2y[/tex]The cost of 3 beef tacos and 1 fruit cup = $ 8.25
[tex]3x+y=8.25[/tex][tex]Substitute\text{ }x=5.25-2y\text{ in the equation.}[/tex][tex]3(5.25-2y)+y=8.25[/tex][tex]15.75-6y+y=8.25[/tex][tex]15.75-5y=8.25[/tex]Add 5y- 8.25 to both sides of the equation
[tex]15.75-5y+5y-8.25=8.25+5y-8.25[/tex][tex]7.5=5y[/tex]Divide both sides by 5.
[tex]\frac{7.5}{5}=\frac{5y}{5}[/tex][tex]1.5=y[/tex][tex]Substitute\text{ }y=1.5\text{ in the equation }x=5.25-2y.[/tex][tex]x=5.25-2(1.5)[/tex][tex]x=2.25[/tex]Final answer:
The price of a beet taco is $ 2.25.
The price of a fruit cup is $ 1.50.
