Answer :
Answer:
a) x is the cost of an apple and y is the cost of a banana.
b)
[tex]4x + 3y = 2.59[/tex]
[tex]6x + 5y = 4.11[/tex]
c) An apple costs $0.31 and a banana costs $0.45.
Step-by-step explanation:
We have to find the cost, in dollars, of an apple and of a banana.
We do this solving a system of equations.
a) Decide on pronumeral names for the unknown quantities.
I am going to say that:
x is the cost of an apple.
y is the cost of a banana.
b).write equations involving these pronunerals.work in terms of dollars.
4 apples and 3 bananas for $2.59
This means that [tex]4x + 3y = 2.59[/tex]
6 apples and 5 bananas for $4.11
This means that [tex]6x + 5y = 4.11[/tex]
c). Solve for the unknowns.
I am going to use the addition method, multiplying the first equation by 5 and the second by -3, and then adding them. So
20x + 15y = 12.95
-18x - 15y = -12.33
20x - 18x + 15y - 15y = 12.95 - 12.33
2x = 0.62
x = 0.62/2
x = 0.31
And
4x + 3y = 2.59
3y = 2.59 - 4x
3y = 2.59 - 4*0.31
3y = 1.35
y = 1.35/3
y = 0.45
An apple costs $0.31 and a banana costs $0.45.