Question

solve the following problems using 5-D process part 2
(Describe/Draw, Define, Do, Decide, and Declare)

a. The number of girls in the Spanish Club is four more than twice the number of boys. There are 61 students in the Spanish Club. Find the number of boys and the number of girls in the Spanish Club.

b. Carrie and John went bowling together. They each bowled one game. Carrie knocked down 12 more pins than John did. The sum of their bowling games was 230. What was Carrie's and John's bowling scores?​

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.