Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. At a candy store, Diana bought 5 pounds of jelly beans and 3 pounds of gummy worms for $58. Meanwhile, Monica bought 6 pounds of jelly beans and 3 pounds of gummy worms for $66. How much does the candy cost? A pound of jelly beans costs $ and a pound of gummy worms costs $ Submit

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EileenJ233514 EileenJ233514 · Answer 1 · 2022-10-30T01:07:38+02:00

Let x be the cost of 1 pound of jelly beans

Let y be the cost of 1 pound of gummy worms

Diana bought 5 pounds of jelly beans and 3 pounds of gummy worms for $58:

[tex]5x+3y=58[/tex]

Monica bought 6 pounds of jelly beans and 3 pounds of gummy worms for $66:

[tex]6x+3y=66[/tex]

[tex]\begin{gathered} 5x+3y=58 \\ 6x+3y=66 \end{gathered}[/tex]

Solve by elimination method:

1. Subtract the equations:

2. Solve x:

[tex]\begin{gathered} -x=-8 \\ x=8 \end{gathered}[/tex]

3. Use the value of x to find y:

[tex]\begin{gathered} 5x+3y=58 \\ 5(8)+3y=58 \\ 40+3y=58 \\ 3y=58-40 \\ 3y=18 \\ y=\frac{18}{3} \\ y=6 \end{gathered}[/tex]

Solution: x=8 y =6

Then, A pound of jelly beans costs $8.00 and a pound of gummy worms costs $6.00