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.

Explanation:

Step1: Find the total number of students with pets

We know that the total number of students is \(104\) and the total number of students with no pets is \(40\). Using the formula \( \text{Total with Pets}=\text{Total Students}-\text{Total with No Pets}\), we have \(104 - 40=64\).

Step2: Find the number of 8th - grade students with pets

We know that the total number of 8th - grade students is \(37\) and the number of 8th - grade students with no pets is \(12\). Using the formula \( \text{8th grade with Pets}=\text{8th grade Total}-\text{8th grade No Pets}\), we get \(37- 12 = 25\).

Step3: Find the number of 7th - grade students with pets

Since the total number of students with pets is \(64\), and the number of 8th - grade students with pets is \(25\). Let \(x\) be the number of 6th - grade students with pets. Let \(y\) be the number of 7th - grade students with pets. But first, assume the number of 6th - grade students with pets is \(a\), 6th - grade total is \(b\).

We know that \(a + y+25=64\). Also, from the total of no - pets: \(10+\text{(7th grade no - pets)}+12 = 40\), so \( \text{7th grade no - pets}=40-(10 + 12)=18\). Since the total number of 7th - grade students is \(46\), using \( \text{7th grade with Pets}=\text{7th grade Total}-\text{7th grade No Pets}\), we have \(46-18 = 28\).

Step4: Find the number of 6th - grade students with pets and total

Since the total number of students with pets is \(64\), and \(25 + 28+\text{(6th grade with Pets)}=64\), so \( \text{6th grade with Pets}=64-(25 + 28)=11\). Then, using \( \text{6th grade Total}=\text{6th grade with Pets}+\text{6th grade No Pets}\), we get \(11 + 10=21\).

Answer:

	Pets	No Pets	Total
7th grade	28	18	46
8th grade	25	12	37
Total	64	40	104