danne9000

You need to know distance from X to michigan to calculate anything of value.

First you find the proportions used

78.94*x+71.94*(1-x)=73.94

78.94*x+71.94-71.94*x=73.94

78.94x-71.94x=73.94-71.94

7x=2

x=2/7

x=0.2857

Multiply this proportion with the overall amount (1000 litres)

and you get

285.714 liters of premium

and 1000-285.714 of regular.

Does simple interest rate mean it's not compounding?

To solve this you have to express the quantities of both as a function of one. For example since the number of bouquets sold was 15 more than the number of hearts, you can express the bouquets as X and then the number of hearts as X-15 rather just Y.

Then you have the following equation.

X*5+(x-15)*3=339

Factor it out to get

5x+3x-45=339

8x=339+45

x=384/8

x=48

y=48-15

y=33

Check it's right by plugging these numbers into the formuler 5x+3y=339

5*48+3*33=339

So they sold 48 roses and 33 hearts. 

Cheers

You have two equations, let games be x and y be rides

5x+6y=28.75

and

4x+3y=16.25

Take the first equation and set x alone on one side of the equation

5x+6y=28.75

5x=28.75-6y <- Divide this by 5 to get x

x=5.75-1.2y

Substitute this for x in the second equation and you get

4x+3y=16.25 becomes...

4(5.75-1.2y)+3y=16.25

23-4.8y+3y=16.25

23-16.25=4.8y-3y

6.75=1.8y

y=3.75

x=5.75-1.2*4

x=1.25

If a 5 foot woman casts a 6 foot shadow then you can calculate how much longer a shadow is than the object as 6/5=1.2

Then you can find the shadow by multiplying 15 by 1.2

Lenght=18 feet

The total minus the fraction sold in the first hour and the remaining fraction after the shift gives you the second hours sales.

I.e. 15/15-(3/15+6/15) => 15/15-9/15=6/15

6/15 sold in the second hour.

 

You'll want to express the number of students in each of the periods as a function of the number of students in a reference period.

Let x be first period, y second periodand z third period

We know what y=2x and z=3x-10

 and x+y+z=158 

Which you can then rewrite as a function of X 

x+2x+3x-10=158

6x-10=158

6x=158+10

x=168/6

x=28

y=2*28

z=28*3-10

So first semester 28 students, second semester 56 students and third semester 74 students.

Cheers

Correct