Question

1. the table shows the amount of money eve earns for different numbers of hours she works.

time eve works (hours) | money eve earns (dollars)
2 1/2 | 26.25
5 | 52.50
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 for every 2/3 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 1/2 hours?

Explanation:

3.

Step1: Calculate unit - rate for Eve

To find the unit rate (amount of money per hour), we can use any row of the table. Let's use the first row where she works $2\frac{1}{2}=\frac{5}{2}$ hours and earns $26.25$ dollars. The unit rate $r$ is calculated as $r=\frac{d}{h}$, so $r = \frac{26.25}{\frac{5}{2}}=26.25\times\frac{2}{5}=10.5$ dollars per hour. The unit rate represents the amount of money Eve earns in one hour of work.

Step2: Write the equation for Eve's earnings

Since the unit rate is $10.5$ dollars per hour, and $d$ is the amount of money she earns and $h$ is the number of hours she works, the equation is $d = 10.5h$.

Step1: Find the rate of bracelet - making for Maya

Maya braids 5 bracelets in $\frac{2}{3}$ hours. The rate $r$ (number of bracelets per hour) is $r=\frac{b}{h}$. So $r=\frac{5}{\frac{2}{3}}=5\times\frac{3}{2}=7.5$ bracelets per hour. The equation representing the number of bracelets $b$ she makes in $h$ hours is $b = 7.5h$.

Step2: Calculate the number of bracelets in $1\frac{1}{2}$ hours

If $h = 1\frac{1}{2}=\frac{3}{2}$ hours, and $b = 7.5h$, then $b=7.5\times\frac{3}{2}=\frac{15}{2}\times\frac{3}{2}=\frac{45}{4}=11.25$ bracelets.

Answer:

a. The unit rate is $10.5$ dollars per hour. It means Eve earns $10.5$ dollars for every hour of work.
b. $d = 10.5h$

4.