Answer: In this question, we are trying to find the difference in price between one apple and one banana. We can set up a system of two equations with two variables to represent the information given in the problem. Let x be the price of one apple in cents and y be the price of one banana in cents.
The first equation represents the information that Dan paid $5.70 for 5 apples and 3 bananas:
5x + 3y = 570
The second equation represents the information that Chris paid $4.70 for 3 apples and 5 bananas:
3x + 5y = 470
We can use these equations to solve for the value of x (the price of one apple) in terms of y (the price of one banana).
We can use the first equation and solve for x:
5x = 570 - 3y
x = (570 - 3y)/5
We can then substitute this expression of x into the second equation:
3((570 - 3y)/5) + 5y = 470
By multiplying both sides of the equation by 5 and 3 respectively, we can get the equation in a form that we can solve for y and then substitute back for x.
We can solve for y by subtracting 3((570 - 3y)/5) from both sides:
5y = 470 - 3((570 - 3y)/5)
Expanding and simplifying the right side of the equation:
5y = 470 - 3(114 - y)
5y = 470 - 342 + 3y
y = (470 - 342)/8
We can substitute this value of y back into the first equation and solve for x
x = (570 - 3y)/5
x = (570 - 3(470 - 342)/8)/5
x = (570 - 441)/5
Therefore, the price of one apple is (570 - 441)/5 = 129 cents more than the price of one banana.
Explanation: