Answer: she would pay $20.14
Explanation:
Let x represent the cost of one pound of orange.
Let y represent the cost of one pound of banana.
If Emily bought three pounds of oranges and four pounds of bananas for $8.53, the expression would be
3x + 4y = 8.53- - - - - - - - - -1
Beth bought four pounds of oranges and two pounds of bananas for $7.74. The expression would be
4x + 2y = 7.74- - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 3, it becomes
12x + 16y = 34.12
12x + 6y = 23.22
Subtracting, it becomes
10y = 10.9
y = 10.9/10
y = 1.09
Substituting y = 1.09 into equation 1, it becomes
3x + 4 × 1.09 = 8.53
3x + 4.36 = 8.53
3x = 8.53 - 4.36
3x = 4.17
x = 4.17/3 = 1.39
For 9 pounds of oranges and 7 pounds of bananas , Jenel would pay
(9 × 1.39) + (7 × 1.09)
= 12.51 + 7.63 = $20.14