Question

At a banquet the ratio of the number of boys to the number of girls is 5:3. Halfway through the banquet 20 boys leave and the ratio becomes 5:4. How many girls are at the banquet?​

Answer 1

let the number of boys be 5x

let the number of girls be 3x

during banket, 20 boys leave

(5x-20)/3x = 5/4

20x - 80 = 15x

5x = 80

x = 16

number of girls is 3x or 48.

check:

original:

boys = 80

girls = 48

after leaving:

boys = 60

girls = 48

ratio is 60:48 = 5 : 4

Answer 2

elinda is thinking about buying a car for $45,000. The table below shows the projected value of two different cars for three years.

Number of years 1 2 3

Car 1 (value in dollars) 40,500 36,450 32,805

Car 2 (value in dollars) 42,000 39,000 36,000

Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

Part C: Belinda wants to purchase a car that would have the greatest value in 13 years. Will there be any significant difference in the value of either car after 13 years? Explain your answer, and show the value of each car after 13 years. (4 points)