I tried this for an hour and could not get it.. Help!?

Question

The difference of two numbers is 39. The larger number is 9 less than 4 times the smaller number. Waht are the two numbers?

Answer 1

let: x=larger number, y=smaller number
x-y=39, difference between the two number
x=4y-9, larger number

substituting,
(4y-9)-y=39
3y=39+9
y=48/3
y=16

x=4(16)-9
x=55

So, the two numbers are 55 and 16.

To check,
x-y=39
55-16=39
39=39

Answer 2

well, you have to convert these words into equations.

let's say x and y are the two unknown numbers.

so... x - y = 39.

and the other information serves as a hint.
The larger number is 9 less than 4 times the smaller number means that x = 4y - 9

so since we have two equations we replace the "x" in x-y = 39 with the 4y-9, which becomes 4y - 9 - y = 39

so solving this : 4y - 9 - y = 39
3y - 9 = 39
3y = 48
y = 16

so we got the value of "y" (or the smaller number)
now to get "x" (or the bigger number) we just plug in y in the first equation, which is x - y = 39

so...x - 16 = 39
x = 39 + 16
x = 55

Now to check this we plug both "x" and "y" to the second equation:
x = 4y - 9
55 = 4(16) - 9
55 = 64 - 9
55 = 55

ANSWER: THE TWO NUMBERS ARE 55 AND 16.

Answer 3

The answers given are unfortunately incorrect. You need to express what you know algebraically, so:

Let x be the larger number and y the smaller. You know the difference is 39, so

x - y = 39

You are also told that the larger is nine less than four times the smaller. "Is" means =, so

x = 4y - 9

You have a set of simultaneous equations, and they're set up for solution by substitution. So - substitute the second equation into the first:

x - y = 39
4y - 9 - y = 39
3y - 9 = 39
3y = 48
y = 16

Finding x:

x = 4y - 9 = 4(16) - 9 = 64 - 9 = 55

Checking:

x - y = 55 - 16 = 39, and it checks. So, the numbers are 55 and 16.

Answer 4

Difference means subtraction. Is means =, less than means to subtract it from something.

The difference of two numbers is 39 written mathematically is:
x-y=39, x is the larger number and y is the smaller number.
The larger number is 9 less than 4 times the smaller number written mathematically is: x=4y-9
After you have these two equations, you plug the second equation into the first and then solve. So start with:
x-y=39, then plug 4y-9 in the equation where x is. So you get:
4y-9 -y=39, then combine like terms. You get:
4y-y -9=39, simplify, you get:
3y-9=39, add 9 to both sides, you get:
3y=48, divide both sides by 3, you get:
y=16
Then go back up to the first equation x-y=39 and plug 16 in for y.
You get: x-16=39. Add 16 to both sides. You get:
x=55

Answer 5

you need a system of equations...
we call the numbers x and y
if the difference between the two is 39 then
x - y = 39

if the larger number (x) is 9 less than 4 times the smaller then
x = 4y - 9

then you solve the system like so:
x= 39 + y
substiture for the x in the second equation
39 + y = 4y - 9
39 + 9 = 4y - y
48 = 3y
y = 48/3
y = 16

now take y and substitute 16 in the original equation
x = 39 + 16
x = 55

check it...
55 - 16 = 39
16 * 4 - 9 = 55

Answer 6

Amber E is almost right, but 49 is 9 MORE than 4 times 10

we want a - b = 39 and a + 9 = 4b

which results in b = 16 and a = 55

Answer 7

if a is larger and b is smaller then a-b=39 and 1-9=4b. Solving the system of equations, you get a=49 and b=10

Answer 8

x: larger number y: smaller number
x - y = 39
x = 4y - 9
4y - 9 - y = 39
3y = 48
y = 16 x = 55

Answer 9

x = smaller number
4x - 9 = larger number

(4x - 9) - x = 39
3x = 48
x = 16

The numbers are 16 and 55

Answer 10

16 and 55