Q9. - Algebra 1

Question

Jane is saving money to buy a new cell phone that costs no more than \(90. So far, she has saved \)52. How much more money does Jane need to save?

1. \(38
2. More than \)38
3. No more than \(38
4. At least \)38

Step-by-Step Solution

Answer

She needs to save no more than $38. Option C is correct.

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{ or }\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b\le c\Rightarrow b\pm a\le c\pm a \\ 2.b\le c\Rightarrow ab\le ac,\text{ if }a>0 \\ 3.b\le c\Rightarrow ab\ge ac,\text{ if }a<0 \end{gathered}$$ 

Step 2. State the inequality from the given information.

Let the amount she needs to save is $x. 

Jane is saving money to buy a new smart phone that costs no more than $90. So far, She saved $52.

She needs $90 and already saved $52.

The inequality:

$52+x\le 90$

Step 3. Solve the inequality .

Solve for x:

$$\begin{gathered} 52+x\le 90 \\ 52+x-52\le 90-52 \\ x\le 38 \end{gathered}$$

She needs to save no more than $38. Option C is correct.