Question

malik is working two summer jobs, making $9 per hour babysitting and making $14 per hour lifeguarding. in a given week, he can work a maximum of 19 total hours and must earn at least $210. if malik worked 4 hours babysitting, determine the minimum number of whole hours lifeguarding that he must work to meet his requirements.

Explanation:

Step1: Define variables

Let \( x \) be the number of hours babysitting and \( y \) be the number of hours lifeguarding. We know \( x = 8 \), total hours \( x + y\leq15 \), and total earnings \( 17x + 10y\geq160 \).

Step2: Substitute \( x = 8 \) into total hours inequality

\( 8 + y\leq15 \), so \( y\leq7 \). But we also have the earnings inequality: \( 17(8)+10y\geq160 \).

Step3: Solve earnings inequality

Calculate \( 17\times8 = 136 \). Then \( 136 + 10y\geq160 \). Subtract 136: \( 10y\geq24 \), so \( y\geq2.4 \). Since hours are whole numbers, the minimum whole number \( y \) is 3. Wait, but wait, the question says "the minimum number of whole hours babysitting that he must work"? Wait, no, he worked 8 hours lifeguarding? Wait, no, the text: "If Malik worked 8 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements." Wait, I misread. Let's correct. Let \( x \) = babysitting hours, \( y = 8 \) (lifeguarding). Total hours: \( x + 8\leq15 \Rightarrow x\leq7 \). Earnings: \( 17x + 10(8)\geq160 \Rightarrow 17x + 80\geq160 \Rightarrow 17x\geq80 \Rightarrow x\geq\frac{80}{17}\approx4.705 \). So minimum whole number \( x \) is 5.

Answer:

5