Need to know the equation for problem

Question

took half as many photos on Friday as on Saturday and took twice as many photos on Sunday than Saturday for a total of 42. How many were taken each day. Know the answer, what is the equation?

Answer 1

This situation can be modeled with a system of equations. Let x = number of photos taken on Friday, y = number of photos taken on Saturday, and z = number of photos taken on Sunday. Then your equations are:

 

x = (1/2)y        ("half as many photos on Friday as on Saturday")

z = 2y        ("twice as many photos on Sunday as on Saturday")

x + y + z = 42        ("a total of 42 photos")

 

 

I know you already have a solution, but I'm guessing you didn't get that by solving the system of equations, so here's how you'd do that. Plug the first two equations into the third equation for x and z, then solve for y:

 

x + y + z = 42

(1/2)y + y + 2y = 42

3.5y = 42

y = 12 photos on Saturday

 

Plug y = 12 back into the first two equations to get x and z:

 

x = (1/2)y

x = (1/2)(12)

x = 6 photos on Friday

 

z = 2y

z = 2(12)

z = 24 photos on Sunday