one number is 4 less than another, if 10 times the smaller number minus 3 times the larger number is 51, find?

Question

one number is 4 less than another, if 10 times the smaller number minus 3 times the larger number is 51, find the two numbers

Answer 1

Calling x the larger number and y the smaller, we have:
y = x-4

Ten times the smaller number minus three times the larger is 51:
10y - 3x = 51

Substitute the first equation value for y into the second:
10(x-4) - 3x = 51
10x - 40 - 3x = 51
7x = 91

x = (91)/(7) = 13

Put the value found for x into the first equation:
y = (x - 4) = (13 - 4) = 9

The two numbers are 13 and 9.

Hope this helps ;)

Answer 2

Set up some algebraic equations, then solve.

Let x be the smaller number and y be the larger number. Since x is 4 less than y,
x + 4 =y.

Now, just read straight through the word problem and convert it to equations. 10 times the smaller number minus 3 times the larger number is 51 is the same thing as saying
10*x - 3*y = 51.

Now, replace y with (x+4).
10*x - 3*(x+4) = 51.

Use the distributive property:
10*x - (3*x + 12) = 51.
10*x - 3*x -12 = 51.

Group x and solve:
7*x - 12 = 51
7*x = 63
x = 9

Now, you know that y is 4 more than x. 9+4 is 13.

So your two numbers are 9 and 13.

Answer 3

Let x equal the smaller number and y the large number, we can set up a number of equations.

y-x=4. (equation 1)

10x-3y=51 (equation 2)

Multiply equation 1 by 10, we have

10y-10x=40 (equation 3)

Add equations 2 and 3 together, we have

10y-3y=40+51=91

7y=91 and y=91/7=13.

Putting 13 into equation 1 yields

13-x=4
Therefore
x=13-4=9.

The small number is 9 , the larger number is 13.

Answer 4

Let x = one of the numbers. Then
x - 4 = the other number

"10 times the smaller number" translates to 10(x - 4)

"minus" means we're subtracting.

"3 times the larger number" translates to 3x.

"is" means equals (or =)

Put it all together and we get

10(x - 4) - 3x = 51. Now we solve for x.

10x - 40 - 3x = 51
7x - 40 = 51
7x = 91
x = 13

That means the two numbers are 13 and 9.

Answer 5

n = smaller number

10n - 3(n+4) = 51
10n - 3n - 12 = 51
7n = 63
n = 9