Question

a random sample of students was surveyed and asked to list their grade level and whether or not they have a pet. results are shown in the table below, but some values are missing. fill in the missing values.
pets
no pets
total
6th grade
7th grade
8th grade
total

Explanation:

Step1: Find the number of 6th - grade students with pets

Use the total number of students with pets ($78$) and the number of 8th - grade ($29$) and 7th - grade ($21$) students with pets.
$$78-(29 + 21)=78 - 50=28$$

Step2: Find the number of 7th - grade students without pets

Use the total number of 7th - grade students (let's find it first). The total number of students is $148$. The number of 8th - grade students is $53$, and the number of 6th - grade students is $44$. So the number of 7th - grade students is $148-(53 + 44)=148 - 97 = 51$. Since there are $21$ 7th - grade students with pets, the number of 7th - grade students without pets is $51-21 = 30$.

Step3: Find the number of 8th - grade students without pets

The number of 8th - grade students is $53$, and the number of 8th - grade students with pets is $29$. So the number of 8th - grade students without pets is $53 - 29=24$.

Step4: Find the number of 6th - grade students without pets

The number of 6th - grade students is $44$, and the number of 6th - grade students with pets is $28$. So the number of 6th - grade students without pets is $44 - 28 = 16$.

Step5: Find the total number of students without pets

Add the number of students without pets in each grade: $24+30 + 16=70$.

Answer:

From left - to - right, top - to - bottom: $28$; $70$; $24$; $30$; $16$