Q63. - Algebra 1

Question

SCHOOL SUPPLIES The table shows the prices of some items Tom needs. If he needs 4 glue sticks, 10 pencils, and 4 notebooks, write and solve an equation to determine whether Tom can get them for under $ 10. Describe what the variables represent.

Step-by-Step Solution

Answer

The required equation is $4x+10y+4z$. The variables represent the cost of each item and the cost is not less than $10.

Step 1. Given.

The table is as follows.

School Supplies Prices
Glue stick	$1.99
Pencil	$0.25
notebook	$1.85

Step 2. To determine.

We have to determine a relation so that Tom can afford each item under $10.

Step 3. Explanation.

Since, Tom needs 4 glue sticks, 10 pencils, and 4 notebooks.

Let us consider the cost price of the glue stick is $x$, cost price of pencil is $y$, and cost price of notebook is $z$.

The total price is the sum of the price of all items.

 

The equation to determine the total price is,

$\text{Total\hspace{0.33em}price}=4x+10y+4z$         

 

Thus, the above equation represents the total price.

 

We put 1.99 for $x$, 0.25 for $y$ and 1.85 for $z$ in the equation.

$$\begin{gathered} 4\left(1.99\right)+10\left(0.25\right)+4\left(1.85\right)=7.96+2.5+7.4 \\ =\$17.86 \end{gathered}$$

 

Hence, the required expression is $4x+10y+4z$. The variable represents cost of the items and the cost is not less than $10.