Question

name
wednesday
for every 8 dogs there are 4 cats in a shelter. if there are 12 more dogs than cats, then how many total animals are in the shelter?
create an equivalent expression for 9(2.5 + 3).
thursday
determine which statement has the same unit rate as $2.50 per ice cream.
a) $7.50 for 3 pies
b) 2.5 lbs for $12.50
c) 1 burger for $2.50
hot dogs are sold in packs of 10 and buns are sold in packs of 8. how many packs of buns and packs of hotdogs will you need to have an equal amount of each?

Explanation:

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Wednesday Top Problem

Step1: Simplify the dog-cat ratio

The ratio of dogs to cats is $8:4$, which simplifies to $2:1$. Let the number of cats be $x$, so the number of dogs is $2x$.

Step2: Set up difference equation

We know dogs are 12 more than cats:
$2x - x = 12$

Step3: Solve for cat count

$x = 12$

Step4: Calculate dog count

Dogs: $2x = 2\times12 = 24$

Step5: Find total animals

Total = $24 + 12 = 36$

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Wednesday Bottom Problem

Step1: Apply distributive property

Use $a(b+c)=ab+ac$:
$9(2.5 + 3) = 9\times2.5 + 9\times3$

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Thursday Top Problem

Step1: Calculate unit rate for a)

$\frac{\$7.50}{3} = \$2.50$ per pie

Step2: Calculate unit rate for b)

$\frac{\$12.50}{2.5} = \$5.00$ per lb

Step3: Identify unit rate for c)

$\$2.50$ per burger

Step4: Match to target rate

Target rate is $\$2.50$ per item, so a) and c) match.

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Thursday Bottom Problem

Step1: Find LCM of 10 and 8

Prime factors: $10=2\times5$, $8=2^3$. LCM = $2^3\times5=40$

Step2: Calculate hot dog packs

$\frac{40}{10}=4$ packs

Step3: Calculate bun packs

$\frac{40}{8}=5$ packs

Answer:

1. Wednesday (top): 36 total animals
2. Wednesday (bottom): $9\times2.5 + 9\times3$ (or simplified: $22.5 + 27$)
3. Thursday (top): a) $\$7.50$ for 3 pies, c) 1 burger for $\$2.50$
4. Thursday (bottom): 4 packs of hot dogs and 5 packs of buns