Mark the number of minutes spent packing the boxes as x. Describe Selma's and Trudy's number of packed boxes in terms of x to make an equation.
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Practice makes perfect
Selma's class is making care packages to give to victims of a natural disaster. We are told that Selma packs one box in 5 minutes and she has already packed 12 boxes. Her friend Trudy packs one box in 7 minutes and has already packed 18 boxes. We want to find the number of minutes both girls need to work in order to have packed the same number of boxes. Let's start with defining x.
x - & the number of minutes spent packing
&the boxes
Let's now express Selma's and Trudy's number of packed boxes in terms of x. Selma packs a box every 5 minutes, so we can assume that she packs 15 of a box every 1 minute. She has already packed 12 boxes, so her amount of packed boxes will be x multiplied by 15 plus 12.
Selma's boxes: 1/5x+ 12
Trudy packs a box every 7 minutes, so we can assume that she packs 17 of a box every 1 minute. She has already packed 18 boxes, so her amount of packed boxes will be x multiplied by 17 plus 18.
Trudy's boxes: 1/7x+ 18
We want the numbers of packed boxes to be equal, so we need to make an equation that will have Selma's boxes on the left-hand side and Trudy's boxes on the right-hand side.
1/5x+ 12 = 1/7x+ 18
Now, we will solve the obtained equation. We will use the inverse operations to combine like terms on both sides of the equals sign and solve for x.
