Question

Theo bakery sells red velvet cakes and cheese cakes in boxes of $12$ at a cost of $\$15$ per box of red velvet and $\$9$ per box of cheese cakes. On Monday and Tuesday, the shop earned $\$396$ by selling a total of $46$ boxes of these two items. If $r$ and $l$ represent the number of boxes of red velvet and cheese cakes respectively, which of the following systems of equations could be used to find the number of boxes of each type of item sold?

• A. $r+l=4615r+9l=396$
• B. $r+l=12\times 4615r+9l=396$
• C. $r+l=4615r+9l=\frac{396}{2}$
• D. $r+l=46\times 1215r+9l=\frac{396}{12}$

Answer 1

The correct option is A $r+l=4615r+9l=396$

Given that a bakery sells red velvet cakes and cheese cakes in boxes of $12$ at a cost of $\$15$ per box of red velvet and $\$9$ per box of cheese cakes

Let he sells $r$ boxes of red velvet's and $l$ boxes of cheeses cakes

Then total boxes $=r+l$

but given sells boxes are $46$

Then $r+l=46...\left(1\right)$

The cost of $r$ red velvet cakes pries $\$15$ per box $=15r$

And cost of $l$ cheese cracks are pries $\$9$ per box $=9l$

But Monday and Tuesday shop eared $\$396$

Then $15r+9l=396...\left(2\right)$

Then equation are

$r+l=46$

$\Rightarrow 15r+9l=396$