danne9000

Let x be large and y be medium, we can write the two totals as

6x+2y=86

4x+3y=72.75

Taking the first equation we can rewrite it to find an expression for x.

6x+2y=86  => 6x=86-2y    < Divide this by 6 and we have x=14.333-0,333y.

Now that we have an expression for x in terms of y, we can subsitute in the second equation as follows

4x+3y=72.75

4(14.33-0.33y)+3y=72.75

57.33-1.33y+3y=72.75

3y-1.33y=72.75-57.33

1.67y=15.42 => y=15.42/1.67

y=9.23

x=14.33-0.33*9.23

x=11.26

Note that I've rounded up to two decimals which creates a slight deviation.

I'm by no means sure but I think it should be 26 options for letters, 5 for even (0,2,4,6,8) and 5 for odd numbers (1,3,5,7,9) and that gives 1 097 500 combinations if I'm not mistaken

So in asile 12 we have 6*24 cupcakes (144) and in aisle 14 we have 8*36 cupcakes (288). Assuming there are no cupcakes in aisle 1-10 or aisle 13 then aisle 11 would have 800-144-288 cupcakes. 

So for this one you'll want to write the equation as follows.

16x+10*(28-x)=400

In other words $16 times the number of scented candles, plus $28 times the total number of sold candles, minus the scented ones sold. We write both as a function of x (x and 28-x) to easily solve it.

After this you factor out the "10(28-x)" part which is 10*28+10*x and solve for X.  Below I'll post the full equation

16x+10(28-x)=400

16x+280-10x=400

16x-10x=400-280

6x=120

x=20

y=8

Check it's correct by 20*16+(28-20)*10=400

Hope it helps

480/52

Let x be the number of women in the senate and y the number of men in the senate.'

We know that y=3x+3     (3 + 3 times the number of women)

We know that x+y=111.

With that you can now substitute y for 3x+3 and get the following:

x+y=111 => x+3x+3=111

4x+3=111

4x=111-3

4x=108

x=108/4

x=27

y=3*27+3 

y=84

Check by 84+27=111

Hope it helps

cheers

If Elena is on page 55 and has read 20 more pages than Andre, it means Andre is on page 35.

If we let x be the number of pages in the book, we can express this as x*0.2=35.  In other words 20% of x is 35.

If x*0.2=35 then x=35/0.2

Cheers

Let x be the number of coach tickets bought. Since we have 8 the number of people who gets first class is 8 minus the number of coach tickets, or 8-x.

With that in mind you can write the equation as 290*x+980*(8-x)=5080.

Factoring gives:

    290x+980*8-980x=5080

    290x-980x+7840=5080

Move the x's to one side and the numbers to the other

980x-290x=7840-5080

690x=2760

x=2760/690

x=4

So that gives 4 coach tickets and 4 first class.

You can double check by 4*980 + 4*290 =5080
 

cheers

Jackies number is x and Adrians is y.
 

y=x-6

x*(x-6)=567

factor out

x^2+6x=567

Set right side to zero

x^2+6x-567=0

Now you want to use AC method and find the two factors that have a difference of 6 and product of 567 (in this case 27 and -21)
Then you can rewrite the equation as x^2+27x-21x-567=0

Factor this out to get x(x+27)-21(x+27)

x is then 27 or -21  and y is 21 or -27

Edit: Missunderstood question, corrected.

Let x be the large number and y the smaller number. we know that 2*x+2*y =310 and that x-y=55 which can also be written as y=x-55

2x+2y=310

Divide by 2

x+y=155

Since y=x-55 we can substitute y for this and get

x+x-55=155

2x=155+55

2x=210

x= 105

y= 105-55 => y=50

Check by 105*2+50*2 => 210+100=310

cheers