Question

1.

time eve works (hours)	money eve earns (dollars)
5	62.50
6	63.00
4 1/5	44.10

a. find the unit rate. explain its meaning in this problem.
b. use the unit rate to write an equation that represents the amount of money eve earns per hour. let h represent the number of hours eve works, and let d represent the amount of money she earns in dollars.

1. maya makes braided bracelets. suppose she works at a constant rate and braids 5 bracelets every 2 hours she works.

a. write an equation that represents the number of bracelets maya braids per hour. let b represent the number of bracelets, and let h represent the number of hours worked.
b. how many bracelets does maya braid in 1 1/3 hours?

Explanation:

Answer:

Question 1a:

• Answer: The unit rate is $10.5$ dollars per hour.
• Explanation:

Step1: Choose a data - point

Let's take the first row where time worked $h = 2.5$ hours and money earned $d=26.25$ dollars.

Step2: Calculate the unit rate

The unit rate (rate of money earned per hour) is found by dividing the money earned by the number of hours worked. So, the unit rate $r=\frac{d}{h}=\frac{26.25}{2.5}=10.5$ dollars per hour. In this problem, it means that for every hour Eve works, she earns $10.5$ dollars.

Question 1b:

• Answer: $d = 10.5h$
• Explanation:

Step1: Use the unit - rate formula

Since the unit rate (rate of money earned per hour) is $10.5$ dollars per hour, and $d$ is the amount of money earned and $h$ is the number of hours worked, the equation representing the relationship is $d=10.5h$ (because the amount of money earned is equal to the rate per hour times the number of hours worked).

Question 2a:

• Answer: $b=\frac{5}{2}h$
• Explanation:

Step1: Find the rate of bracelet - making per hour

Maya braids 5 bracelets in 2 hours. The rate of bracelet - making per hour is $\frac{5}{2}$ bracelets per hour. If $b$ is the number of bracelets and $h$ is the number of hours worked, the equation is $b=\frac{5}{2}h$ (using the formula $b = rh$, where $r$ is the rate).

Question 2b:

• Answer: $\frac{25}{6}$ bracelets
• Explanation:

Step1: Substitute the value of $h$ into the equation

We have the equation $b=\frac{5}{2}h$. Given $h = 1\frac{2}{3}=\frac{5}{3}$ hours. Substitute $h=\frac{5}{3}$ into the equation: $b=\frac{5}{2}\times\frac{5}{3}=\frac{25}{6}$ bracelets.