Q45. - Algebra 1

Question

Pilar bought 17 items for her camping trip, including tent stakes, packets of drink mix, and bottles of water. She bought 3 times as many packets of drink mix as tent stakes and 2 more bottles of water than tent stakes. Write and solve the equation to discover how many tents stakes Pilar bought.

Step-by-Step Solution

Answer

The number of tents stakes is 3.

Step 1. Given information.

Pilar bought 17 items for her camping trip, including tent stakes, packets of drink mix, and bottles of water.

Step 2. Mention the variables.

Consider the number of tent stakes be t, a number of packets of drink mix are p, and a number of water bottles are w.

So, from the given information:

$t+p+w=17$

Step 3. Write the equation.

Since Pilar bought 3 times as many packets of drink mix as tent stakes.

So,

$3t=p$

Again, Pilar bought 2 more bottles of water than tent stakes.

So,

$t+2=w$

Step 4. Solve equations.

Substitute $p=3t$ and $t+2=w$ in the equation $t+p+w=17$.

$$\begin{gathered} t+p+w=17 \\ t+3t+t+2=17 \\ 5t+2=17 \end{gathered}$$ 

Solve this equation below.

 $$\begin{gathered} 5t=17-2 \\ 5t=15 \\ t=3 \end{gathered}$$