Read this article and watch the video. The article describes examples in which systems of equations can be used to solve real-world quantities. After you review, complete problems 1 to 4 and check your answers.
Example
Example 1
A baker sells plain cakes for $7 and decorated cakes for $11. On a busy Saturday the baker started with 120 cakes, and sold all but three. His takings for the day were $991. How many plain cakes did he sell that day, and how many were decorated before they were sold?
plain cakes | decorated cakes | total | |
---|---|---|---|
Cakes sold | p | d | \(\begin{align*} 120-3=117\end{align*}\) |
Cost of cakes | 7p | 11d | $991 |
The system of equations that describes this problem is:
\(\begin{align*}p+d=117\!\\ 7p+11d=991\end{align*}\)
Let's solve this system by substituting the second equation into the first equation:
\(\begin{align*}p+d=117 \Rightarrow p=117-d\end{align*}\)
\(\begin{align*}7p+11d=991 & \Rightarrow 7(117-d)+11d=991\\ & \Rightarrow 819-7d+11d=991\\ & \Rightarrow 819+4d=991 \\ & \Rightarrow 4d=172 \\ & \Rightarrow d=43\end{align*}\)
We can substitute \(\begin{align*}d\end{align*}\) into the first equation to solve for \(\begin{align*}p\end{align*}\).
\(\begin{align*} p=117-d=117-(43)=74\end{align*}\)
The baker sold 74 plain cakes and 43 decorated cakes.