if the larger of two numbers is subtracted from 6 times the smaller, the result is 20. If twice the larger num

Question

if the larger of two numbers is subtracted from 6 times the smaller, the result is 20. If twice the larger number is added to 4 times the smaller, the result is 56. Find the numbers.

Answer 1

Let the numbers be x and y,x being the larger
According to the conditions of the problem
6y-x=20.......(equation 1)
2x+4y=56.....(equation 2)
From 1,
-x=20-6y
=>x=6y-20
Plug in the value of y in equation 2
2(6y-20)+4y=56
12y-40+4y=56
16y=56+40
y=96/16=6
Plugging the value of y
x=6*6-20
=36-20=16
the numbers are 16 and 6

Answer 2

Let L=larger number
S=smaller number

Then the mathematical expression for "larger of two numbers subtracted from 6 times the smaller, the result is 20" is:

6(S) -L = 20 - - - - equation (1)

and for "twice the larger number is added to 4 times the smaller, the result is 56" is:

2(L) + 4(S) =56 - - - equation (2)

Solving for L in equation (1) yields:

L = 6(S) - 20 - - - - equation (1a)

Substituting the value of L in equation (1a) to equation (2) yields:

2[ 6(S) - 20 ] + 4(S) = 56
12(S) - 40 + 4(S) = 56
16(S) = 56 +40
S = 96/16
S = 6

Using the value of S in solving for L in equation (1a) yields:

L = 6(6) - 20
L = 16

Therefore,

Larger Number L = 16
Smaller Number S = 6

Answer 3

This one time, I'll actually work the problem, even though you're obviously a student asking us to do a homework problem for you. I assume you have other problems to do, so you can use this one as an example.

Choose M as the variable representing the bigger number.
Choose N as the variable representing the smaller number.
(You could choose any letters; I chose these two.)

Always write the times/multiplication parts first.

6N is the same as "6 times the smaller".
Then you want to subtract M from that.

6N - M is the same as:
"the larger of two numbers is subtracted from 6 times the smaller".

So:

6N - M = 20

THEN, find the second equation:
(remember? Find the mulitiplication first!)

2M is the same as "twice the large number".

4N is the same as "4 times the smaller".

So:
2M + 4N = 56 is the same as
"twice the larger number is added to 4 times the smaller, the result is 56."

THEN, solve one of the equations for one of the variables. It doesn't matter which variable you choose. I chose to solve the first equation for M.

6N - M = 20

Add M to both sides.

6N = 20 + M

Subtract 20 from both sides.

6N - 20 = M

THEN, plug the left side into the other equation everywhere you see an M.

2M + 4N = 56

becomes

2 (6N - 20) + 4N = 56

Multiply out, then solve:

12N - 40 + 4N = 56

Add 40 to both sides.

12N + 4N = 96

Combine like terms (add the Ns together)

16N = 96

Divide both sides by 16.

16N / 16 = 96 / 16

N = 6


So, the smaller number is 6.

THEN, plug 6 into the first equation where ever you see N.

6 (6) - M = 20

36 - M = 20

Add M to both sides.

36 = 20 + M

Subtract 20 from both sides.

16 = M

16 is the bigger number.

Answer 4

Let a and b the larger and smaller numbers.

6b - a = 20

2a + 4b = 56

-2a + 12b = 40 (mutlitplying the first by 2)

Adding the two, we get

16b = 96

b = 96 / 16 = 6

-2a + 72 = 40

-2a = 40 - 72 = - 32

a = 16

So, 16 and 6 are the two numbers.

Answer 5

let the larger no be x and the smaller no be y

6y - x = 20
4y + 2x = 56

solve simultaneously to get x = 16 and y =6