Question

Solve the following problems using 5-D process part 2

Answer 1

The two problems are almost identical: you have to set up a system, and then solve it.

In the first case, let $g$ and $b$ be, respectively, the number of girls and boys.

We know that $g=2b+4$ (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that $g+b=61$ (there are 61 students in total).

So, we have the system

$\begin{cases}g=2b+4\\g+b=61\end{cases}$

We can use the first equation to substitute in the second

$g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19$

And then solve for $g$:

$g=2b+4=2\cdot 19+4=38+4=42$

For the second problem, let $c$ and $j$ be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system

$\begin{cases}c=j+12\\c+j=230\end{cases}$

And you can solve it in the very same way we solved the previous one.