Mark and his friends order two pizzas of the same size. . The first pizza is cut into 6 slices of equal size. . The second pizza is cut into 4 slices of equal size. Each person plans to take 2 slices of pizza. Mark concludes that he would get more pizza by taking 1 slice from each pizza, instead of 2 slices from the first pizza. Explain why Mark is correct. Be sure to include a number comparison using > or < in your explanation.

Both pizzas have same size.

The first pizza is cut into 6 slices of equal size. 

Each slice of first pizza = 1/6 of pizza  

The second pizza is cut into 4 slices of equal size.

Each slice of second pizza = 1/4 of pizza  

1/4>1/6 

So slice of second pizza is greater than that of  first pizza.

Part of pizza Mark got when he pick 2 Slices from the first pizza = 2×1/6 = 1/3 of pizza 

Part of pizza Mark got when he pick 1 slice from each pizza = 1/6 + 1/4 

= (2+3)/12 

= 5/12 of pizza 

For comparing 1/3 and 5/12 we need to make the denominator of both numbers  equal. 

To make denominator equal we have to multiply 1/3 from 4/4, 

1/3×4/4 = 4/12 

4/12<5/12 (when the denominator of two numbers is same the number with greater numerator is greater)

So mark was right

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

The answer is in the image 

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Area of rectangle= L*b

here,

L=12.4 cm

b= 8.8 cm

A= L*b

= 12.4 * 8.8 = 109.12 cm^2

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years