The most popular items at a bakery are its raspberry scones and its lemon poppy seed muffins. The shop sells both items in boxes of 12 at a cost of $15 per box of raspberry scones and $9 per box of lemon poppy seed muffins. On Friday and Saturday, the shop earned $396 by selliing a total of 46 boxes of these two items. If r and l represent the number of boxes of raspberry scones and lemon poppy seed muffins sold over the two-day period, respectively, which of the following systems of equations could be used to find the number of boxes of each type of item sold?

Options

A. `r+l=46`
`15r+9l=396`
B. `r+l=12times46`
`15r+9l=396`
C. `r+l=46`
`15r+9l=(396)/(2)`
D. `r+l=12times46`
`15r+9l=(396)/(12)`

Answer

A

Explanation

Difficult: Medium
Category: Heart of Algebra/ System of Linear Equations
Strategic Advice: In a lengthy word problem that contains lots of numbers, it may help to cross out information that does not impact the answer.
Getting to the Answer: Here, the number of items in each box does not matter because the entire questions is about the boxes of items (not the number of items), so cross out the 12. This means you can eliminate B and D right away. The question states that r and l represent the number of boxes of raspberry scones and lemon poppy seed muffins sold and that the shop sold a total of 46 boxes of these items, so the first equations will be r+l=46. The shop collects $15 for each boc of raspbarry scones, which translates to 15r, and $9 for each box of lemon poppy seed muffins, which becomes 9l. Put together,the second equation is `15r+9l=396`, making (A) the correct answer. Note that because the question doesn't ask about the number sold per day, you don't need to incorporate a 2 into either equation.