Q 349 - Intermediate Algebra

Question

In the following exercises, translate to a system of equations and solve. 

Mollie wants to plant $200$ bulbs in her garden, all irises and tulips. She wants to plant three times as many tulips as irises. How many irises and how many tulips should she plant? 

Step-by-Step Solution

Answer

Mollie should plant $50$ irises and $150$ tulips.

Step 1. Identify and name what we are looking for.

We need to find how many tulips and irises do Mollie plant.

Let $x$ represents the number of iris plants planted and $y$ represents the number of tulip plants planted.

Step 2. Form the equation

The total number of plants planted is $200$. So the first equation is

$x+y=200 ...\left(1\right)$

Also, the number of tulips plants is three times the number of irises. So the second equation is

$y=3x ...\left(2\right)$

Step 3. Solve using substitution

Using the second equation substitute $3x$ for $y$ in the first equation and solve for $x$

$\begin{array}{rcl}x+y& =& 200\\ x+3x& =& 200\\ 4x& =& 200\\ x& =& 50\end{array}$

Now substitute $50$ for $x$ in the second equation.

$$\begin{gathered} y=3x \\ y=3\times 50 \\ y=150 \end{gathered}$$

So the number of irises planted is $50$ and the number of tulips planted is $150$.

Step 4. Check the solution

Substitute $50$ for $x$ and $150$ for $y$ in the first equation formed.

$\begin{array}{rcl}x+y& =& 200\\ 50+150& =& 200\\ 200& =& 200\end{array}$

It is a true statement.

Again, substitute the values in the second equation formed.

$\begin{array}{rcl}y& =& 3x\\ 150& =& 3\times 50\\ 150& =& 150\end{array}$

This is also a true statement.

So the point satisfies both the equations.