Question

Choose all situations that state or apply the correct unit rate. If Sara pays $9.75 for 5 cupcakes, the price of each cupcake is $1.75. John earns $280 for mowing 8 lawns. At the same rate he will earn $350 for mowing 10 lawns. Kayla pays $140 for 10 yoga classes. At the same rate, she will pay $168 for 12 classes. Keisha pays $12.50 for 10 cups of coffee each week. At the same rate, Keisha can buy 7 cups of coffee for $8.75. Ian bikes 60 miles in 5 days. The unit rate is 14 miles each day.

Answer 1

Answer:

The first one does NOT apply: $9.75 / 5 = $1.95

The second one does apply: $280 / 8 = $35    and $350 / 10 = $35

The third one does apply: $140 / 10 = $14 and $168 / 12 = $14

The fourth one does apply: $12.50 / 10 = $1.25 and $8.75 / 7 = $1.25

The fifth one does NOT apply: 60 / 5 = 12

Hope this helps!

Answer 2

Rate is the measure of increment in number of dependent quantity per unit independent quantity. The situations having correct unit rate are:

• Case 2: John earning from mowing lawns
• Case 3: Kayla paying for yoga classes
• Case 4: Keisha buying cups of coffee.

What is unit rate?

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

For the given cases, we have:

• Case 1: Sara pays $9.75 for 5 cupcakes.

It means

$5 \: \rm cupcakes = \ 9.75\\\text{Dividing both the quantities by 5}\\\\1 \: cupcake = \ 9.75/5 = \ 1.95$

(we equated both quantities on deal level(deal is made by thinking that 5 cupcake will be equal to $9.75))

The rate of price (dependent quantity) of 1 cupcake(quantity of cupcake is independent quantity as it comes first, without any effect of price(assuming)) is $1.95, and not $1.75

Thus, the rate given is wrong in this case.

• Case 2: John earns $280 for moving 8 lawns

It means

$\ 280 \: \rm earned = 8 \: lawns \: mowed\\\\\\\text{Dividing both quantities in 8 parts}\\\\\dfrac{280}{8} = \ 35 = 1 \: lawn \: mowed$

Thus, mowing 1 lawn will make John earn $35.

For 10 such mowing, he will get $35 + $35 .. + 35  (10 times) = 35×10 = $350

Thus, as it is given that "At the same rate he will earn $350 for mowing 10 lawns", thus, thus case is correctly using rate of amount earned per unit lawn mowed.

Similarly,

• Case 3:

$140 = 10 yoga classes

Dividing in 10 parts

$14 = 1 yoga class

(rate is $14 per unit (single) yoga class)

Multiplying with 12, we get:

$168 = 12 yoga classes.

Thus, its equal to given quantity and thus, this case is correctly using the unit rate,

• Case 4:

$12.50 = 10 cups,

$1.25 = 1 cup

For 7 cups, Multiply with 7,

$8.75 = 7 cups,

Thus, given rate $8.75 per 7 cup is correct.

• Case 5:

60 miles = 5 days

12 miles = 1 day

So unit rate is 12 miles each day and not 14 miles each day. So this case calculates wrong unit rate.

Thus,

The situations having correct unit rate are:

• Case 2: John earning from mowing lawns
• Case 3: Kayla paying for yoga classes
• Case 4: Keisha buying cups of coffee.

Learn more about rate of change here:

https://brainly.com/question/11484885