Nicole runs a farm stand that sells bananas and peaches. each pound of bananas sells for $2 and each pound of peaches sells for $3.25. nicole sold 3 more pounds of bananas than pounds of peaches and made $231.75 altogether. write a system of equations that could be used to determine the number of pounds of bananas sold and the number of pounds of peaches sold. define the variables that you use to write the system.

The required system of equations is:

2x + 3.25y = 231.75

x = y + 3

where x is the number of pounds of bananas and y is the number of pounds of peaches

Explanation:

1- Defining the variables:

Assume that the number of pounds of bananas sold is x

Assume that the number of pounds of peaches sold is y

2- Setting the system of equations:

We are given that:

i. Each pound of bananas sells for $2

  Money gained from selling x pounds of bananas is 2x

ii. Each pound of peach sells for $3.23

   Money gained from selling y pounds of peaches is 3.25y

iii. Nicole made $231.75 in total. This means that:

    2x + 3.25y = 231.75 > equation I

iv. Nicole sold 3 more pounds of bananas than pounds of peaches. This

    means that:

    pounds of bananas = pounds of peaches + 3

    x = y + 3 > equation II

3- Solving the equations (if required):

In equation II, we have: x = y + 3

Substitute with equation II in equation I and solve for y as follows:

2x + 3.25y = 231.75

2(y+3) + 3.25y = 231.75

2y + 6 + 3.25y = 231.75

5.25y = 231.75 - 6

5.25y = 225.75

y = 43

Substitute with y in equation II to get x:

x = y + 3

x = 43 + 3 = 46

Based on the above:

Number of pounds of bananas = x = 46 pounds

Number of pounds of peaches = y = 43 pounds

Hope this helps :)

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