<u><em>Answer:</em></u>
<u>The required system of equations is:</u>
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
<u><em>Explanation:</em></u>
<u>1- Defining the variables:</u>
Assume that the number of pounds of bananas sold is x
Assume that the number of pounds of peaches sold is y
<u>2- Setting the system of equations:</u>
<u>We are given that:</u>
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. <u>This means that:</u>
2x + 3.25y = 231.75 .................> equation I
iv. Nicole sold 3 more pounds of bananas than pounds of peaches. <u>This</u>
<u>means that:</u>
pounds of bananas = pounds of peaches + 3
x = y + 3 ..................> equation II
<u>3- Solving the equations (if required):</u>
In equation II, we have: x = y + 3
<u>Substitute with equation II in equation I and solve for y as follows:</u>
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
<u>Substitute with y in equation II to get x:</u>
x = y + 3
x = 43 + 3 = 46
<u>Based on the above:</u>
Number of pounds of bananas = x = 46 pounds
Number of pounds of peaches = y = 43 pounds
Hope this helps :)
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