A teacher needs to purchase notebooks and pencils for her students. Notebooks come in packages of 6 and pencils in packages of 10. The table shows the cost of the items. What is the least amount of money the teacher can spend and have the same number of notebooks and pencils.

$31.00

Step-by-step explanation:

Given:

We need to find the LCM of 6 and 10:

Multiples of 6:  6, 12, 18, 24, 30

Multiples of 10: 10, 20, 30

Therefore, the LCM = 30

So the least number of notebooks and pencils the teacher can buy to have the same numbers of each is 30.

⇒ 30 ÷ 6 = 5 packages of notebooks

⇒ 30 ÷ 10 = 3 packages of pencils

5 packages of notebooks = 5 × $5.00 = $25.00

3 packages of pencils = 3 × $2.00 = $6.00

Therefore, the least amount of money the teacher can spend to have the same number of notebooks and pencils (30 each) is:

⇒  $25.00 + $6.00 = $31.00

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.