Answer:
[tex]x+y=12[/tex]
[tex]0.4x+0.5y=5.70[/tex]
Step-by-step explanation:
Given :
Larji bought a dozen ears of corn.
She prefers yellow corn, which costs 40 cents an ear, and her siblings prefer the peaches and cream variety, which costs 50 cents an ear.
She buys a mixture of each type and pays $5.70.
To Find: Which system of equations represents the number of ears of corn of each type that Larji purchased?
Solution:
We are given that Larji bought a dozen ears of corn.
So, Number of ears of corn bought by Larji = 1 dozen = 12
Let x be the number of yellow corn.
let y be the number of peaches and cream variety corn
Now we are given that he bought 12 number of ear corns
So, x+y=12 ---1
Now cost of 1 ear of Yellow corn = 40 cents
1 cent = 0.01 dollars
So, 40 cents = [tex]40 \times 0.01=0.4 dollar[/tex]
Cost of 1 ear of Yellow corn = $0.4
Cost of x ear of Yellow corn = $0.4x
Cost of 1 ear of peaches and cream variety corn = 50 cents
50 cents = [tex]50 \times 0.01=0.5 dollar[/tex]
Cost of 1 ear of peaches and cream variety corn = $0.5
So, Cost of y ear of peaches and cream variety corn =$0.5y
Since we are given that She buys a mixture of each type and pays $5.70.
So, equation becomes : [tex]0.4x+0.5y=5.70[/tex]--2
Thus the system of equations represents the number of ears of corn of each type that Larji purchased is :
[tex]x+y=12[/tex]
[tex]0.4x+0.5y=5.70[/tex]
