Question

Theo bakery sells red velvet cakes and cheesecakes in boxes of 12 at a cost of \[$15\] per box of red velvet cake and 9 per box of cheesecakes on Monday and Tuesday the shop earned \[$396\] by selling a total of 46 boxes of these 2 items. If s and l represent the number of boxes of red velvet and cheesecake respectively which of the following systems of equations could be used to find the number of boxes of each type of item sold?

A) $\begin{align}
  & r+l=46 \\
 & 15r+9l=396 \\
\end{align}$

B) $\begin{align}
  & r+l=12\times 46. \\
 & 15r+9l=396 \\
\end{align}$

C) \[\begin{align}
  & r+l=46 \\
 & 15r+9l=\dfrac{396}{2} \\
\end{align}\]

D) $\begin{align}
  & r+l=46\times 12 \\
 & 15r+9l=\dfrac{396}{12} \\
\end{align}$

Answer 1

Hint: First equation will be for the total number of cake boxes sold on those two days and the second equation will be from the money earned on Monday and Tuesday from each box of cake.

Complete step by step solution: The bakery sells red velvet cakes and cheesecake in boxes of 12.
Cost of a box of red velvet cake = 5
Cost of a box of cheesecake= 9
Also, it is given that they sold r boxes of red velvet cake and l boxes of cheesecake.
And on Monday and Tuesday the shop earned 396 dollars.
Now, the total boxes sold= $r+1$
and given that a total 46 boxes are sold. so
$r+l=46$----(1)
Let the rate of velvet cake be 15 per box = 15r
and the rate of l cheese cake at 9 per box = 9l.
Also, on Monday and Tuesday the shop earned 396 dollars. therefore,
$15r + 9l = 396$ (2)
Hence the equation are:
$r + l = 46$
and
$15r + 9l = 396$

Hence, option A is the correct option.

Note: In this type of question follow the question and accordingly make an equation to solve. Also, to get the value of r and l in this question we can apply 2 equations-2 variable methods. It’s important to know that we always try to make as many equations as unknowns we have.