Question

1. a track team decreases the speed they run by 1.2 yards. they decrease the speed they run by another % yard
2. alya feeds her hamster 7/9 tablespoon of hamster food 3 times a day.

• darla feeds her hamster 2 times each day.
• she gives her hamster equal amounts of hamster food each time she feeds it.
• the amount of hamster food darla feeds her hamster each day is equal to 70% of the amount of hamster food alya feeds her hamster each day.

how many tablespoons of hamster food does darla give her hamster each time she feeds it?

1. which equations are shown with the correct solutions?

select the three correct equations with correct solutions.
a. ⅔ x - 2 = 10, where x = 18
b. 6x + 4 = 406, where x = 6
c. ¼ x + 5 = 9, where x = 16
d. 7x - 3 = 46, where x = 7
e. 3x - ½ = 8.5, where x = 3

1. an expression is shown.

¼ (16.8 +7.2) + 3.5
part a
maya starts to evaluate the expression.
step 1: ¼ +7.2+3.5
the expression maya wrote for step 1 is incorrect. explain how to correct the error in step 1.
enter your explanation in the box provided.
10.
part b
find the value of the expression ¼ (16.8 +7.2) + 3.5
show or explain your work.
enter your answer and your work or explanation in the box provided.

Explanation:

Problem 8

Step1: Calculate Mya's daily food

Mya feeds $\frac{7}{9}$ tbsp 3 times a day:
$\frac{7}{9} \times 3 = \frac{21}{9} = \frac{7}{3}$ tablespoons per day

Step2: Find Daria's daily food

Daria's daily amount is 70% of Mya's:
$0.7 \times \frac{7}{3} = \frac{7}{10} \times \frac{7}{3} = \frac{49}{30}$ tablespoons per day

Step3: Calculate Daria's per-feeding amount

Daria feeds 2 times a day:
$\frac{49}{30} \div 2 = \frac{49}{30} \times \frac{1}{2} = \frac{49}{60}$

Step1: Check Option A

Substitute $x=18$: $\frac{2}{3}(18)-2 = 12-2=10$. Correct.

Step2: Check Option B

Substitute $x=6$: $6(6)+4=36+4=40
eq 406$. Incorrect.

Step3: Check Option C

Substitute $x=16$: $\frac{1}{4}(16)+5=4+5=9$. Correct.

Step4: Check Option D

Substitute $x=7$: $7(7)-3=49-3=46$. Correct.

Step5: Check Option E

Substitute $x=3$: $3(3)-\frac{1}{2}=9-0.5=8.5$. Correct.
(Note: The question asks for 3 correct equations; A, C, D are valid choices, or A, C, E, but per selection of 3, the confirmed correct ones are A, C, D)

Maya violated the distributive property. When expanding $\frac{1}{4}(16.8 + 7.2)$, she must multiply both terms inside the parentheses by $\frac{1}{4}$, not just omit the first term. The correct Step 1 should distribute $\frac{1}{4}$ to 16.8 and 7.2.

Answer:

$\frac{49}{60}$ tablespoons

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Problem 9