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Multiply the top numbers together.

Multiply the bottom numbers together.

Divide the top result by the the bottom result.

Just multiply them together.

The graph I made for your question did not save whenever I tried to put the link in, so what you do is you can go to Deimos or geoDebra,put that equation in and you should have the answer.sorry about that :)

So for this question,x will be your starting amount and y will be your brothers. 

So both the following equations are true. 

x-5 = y+5 

2(y-25) = x+25 

First we will start with the 2nd equation 2(y-25) = x+25 

Firstly,we will do 2y=x+75, which will get us y=1/2x+37.5.

Now we do the first equation which is x-5=y+5, which will give us x=y+10 and plug both into the old equation,which will give us:

y = 1/2(y+10) + 37.5 

y = 1/2y+5+37.5

y = 1/2y + 42.5 

1/2y = 42.5 

y = 85

So logically, X should equal 95

The answer is 85. 

R==Roses,   C ==Carnations

C / R==3/1.....................(1)

3R  + 1.5C==18..............(2), solve for C, R

C==36/5  and  R==12/5  [You cannot have fraction of a flower! Therefore I cannot see a viable solution if he wants to spend all his money on flowers and have 3 times as many carnations as roses]

See this solution here:  https://web2.0calc.com/questions/need-help-with-system_6

a + ab = 250,   

a - ab = -240

Add the 2 equations together:

2a == 10

a ==10 / 2 ==5

Sub the value of a in the first equation:

5 + 5b ==250

5b ==250 - 5 ==245

b==245 / 5 ==49

So, the values of a, b==(5, 49)

a = 3, b = -7

Let the initial number of orange trees =T

210* [T - 5] ==41,790

210T  -  1050 ==41,790

210T =41,790 + 1050

210T ==42,840

T ==42,840 / 210

T ==204 - original number of orange trees on MacDoald's farm

Check: [204 - 5] * 210 ==41,790 - which balances.

i see now, thank you very much!

i see now, thank you very much!

The coefficient of y^4 is 80.

An aquarium tank is 1/6 full of water. When 2 gallons of water are added, the tank becomes 1/2 full. What is the total capacity of the aquarium tank, in gallons?   

Note that 1/2 is the same as 3/6.  

So 2 gallons added 2/6.  That means 1 gallon is 1/6.  

Therefore, the total capacity of the aquarium is 6 gallons.  

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

Consider                                                                ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

For certain values of k and m, the system

3a + 2b = 2

6a + 2b = k + 3a + mb

has infinitely many solutions (a,b).  What are k and m?   

The problem states that  

                                                              6a + 2b  =  k + 3a + mb  

If you subtract 3a from both sides  

                                                              3a + 2b  =  k + mb  

The problem also states that  

                                                              3a + 2b  =  2  

From which it follows that  

                                                               k + mb  =  2  

Therefore  

                                                                       k  =  2 – mb  

and  

                                                                                2 – k 

                                                                       m  =  ———  

                                                                                   b 

_.

k = -1, m = 8

(a,b,c,d,e) = (-1,4,7,8,5)

The formula for a geometric sequence is an​=a1​rn−1, where a1​ is the first term, r is the common ratio, and n is the term number.

We know that g23​=16 and g28​=24. We can use these values to find the common ratio r.

g28​ = g23 r^{28 - 23} 24 = 16r^5 r^5 = 2 r = 2^(1/5)

Now that we know the common ratio, we can find g43​.

g43​=g23r^{43-23} g43 = 16*(2^{1/5})^(43-23) g43 = 16*(2^(1/5))^20 g43 = 16*2^4 g43 = 128

Therefore, g43​=128.

Betty's 120,000 falls into the 85,526 < d < 163,300 bracket  

So her tax is figured as  

                                                              0.24(120,000 – 85,525) + 14,605.5  

From there it's  

just arithmetic ....  

                                                              0.24(34,475) + 14,605.5  

                                                              8,274 + 14,605.5  

Betty's tax, in dollars, is  

                                                              22,879.50 dollars   

_.

no, it is not

A candy bar and a piece of bubble gum together cost 1.50.  The candy bar costs a dollar more than the bubble gum.  How much does the piece of bubble gum cost, in cents?   

                                                                      C + B  =  1.50  

                                                                      C – B  =  1.00  

Just subtract the second from the first               2B  =  0.50  

                                                                            B  =  0.25  =  25¢  

_.

(e-8)*3=e-5  

Multiply it out                                        3e – 24  =  e – 5  

Add 24 to both sides                            3e          =  e + 19  

Subtract e from both sides                   2e          =        19  

Divide both sides by 2                                   e  =  9.5  

_.

Think in terms of shovels.

If the father can dig, on average, f shovels per hour and it takes W shovels to dig the well, it would take the father, working alone, W/f hours to dig the well.

Similarly if the son can dig, on average, s shovels per hour, it would take him, working alone W/s hours to dig the well, (and notice in passing that this is the number to be calculated).

Now, the well can be dug if the father works for 6hrs and the son for 12 hrs, so

6f + 12s = W

and similarly

9f + 8s = W.

Multiply the first equation by 3 and the second by 2,

18f + 36s = 3W

18f + 16s + 2W,

and subtract,

20s = W,

so W/s = 20.

S = 77 + 154 + 231 + ... = 1*77 + 2*77 + 3*77 + ...

10,000/77 = 129.87

129*77 = 9933

130*77 = 10,010

S = 1*77     + 2*77     + 3*77     + ... + 129*77

S = 129*77 + 128*77 + 127*77 + ... + 1*77

Add

2S = 130*77 + 130*77 + 130*77 + ... + 130*77

     = 129*130*77

S  =  129*130*77/2 = 645645.

a=tens digit,  b=ones digit

10*a + b ==10*b + a + 45...............(1)

a ==2*b - 1......................................(2), solve for a, b

a==11 and b==6 - this solution does not work since a is a 2-digit number.

Try: b=2*a - 1 which gives:

a=-4  and  b ==-9

[-4 * 10 - 9] == - 49 - which appears to be Sophie's favorite number.

Check: -49 - ( - 94) ==45 - difference between them

              [2 * - 4] == - 8 which is 1 greater than - 9 or - 9 is one less that double the other (2 * - 4) = -8