Question

Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save.

a + 212 greater-than-or-equal-to 365

If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why?
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
No, because he needs to save $577, and he will only save $150 more.
Yes, because he has already saved $365, and the stereo cost $212.
Yes, because he has already saved $212, and he will save another $150

Answer 1

A) No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.

Explanation:

The given inequality represents the amount Ben still has to save to be able to buy the new car stereo:

`a + 212 \geq 365`

where:

• "a" is the amount Ben still has to save.
• 212 is the amount (in dollars) he has already saved.
• 365 is the cost (in dollars) of the new car stereo.

To calculate how much Ben still needs to save, solve the inequality:

`\begin{aligned}a + 212& \geq 365\\a + 212-212& \geq 365-212\\a&\geq153 \end{aligned}`

Therefore, Ben needs to save at least $153 to be able to buy the new car stereo.

If Ben saves $15 a week for the next 10 weeks, he will save a total of $150:

`\$15 * 10=\$150`

As $150 is less than $153, and he needs to save at least $153, he will not have enough money to buy the new car stereo.

Therefore, the correct answer is:

• No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.