The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.
What is a system of equation?
A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.
For the given situation,
Peter sold a cup of lemon juice = $1.25
Peter sold a cup of apple juice = $2.50
Total number of cups sold = 155 cups
Total amount = $256
Let number of cup of lemon juice be x and
let number of cup of apple juice be y
The equations for the above statements are
[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]
From equation 1,
⇒ [tex]x=155-y[/tex]
Now substitute x in equation 2,
⇒ [tex]1.25(155-y)+2.50y=256[/tex]
⇒ [tex]193.75-1.25y+2.50y=256[/tex]
⇒ [tex]1.25y=256-193.75[/tex]
⇒ [tex]1.25y=62.25\\[/tex]
⇒ [tex]y=\frac{62.25}{1.25}[/tex]
⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]
Now substitute y in equation 1,
⇒ [tex]x=155-50[/tex]
⇒ [tex]x=105[/tex]
Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.
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