The larger of 2 numbers is 11 less than 3 times the smaller. The sum is 69. what are the numbers?

Question

The larger of 2 numbers is 11 less than 3 times the smaller.  The sum is 69.   what are the numbers?

Avery Alexander · Accepted Answer

#color(magenta)(x=20# Let the no.s be #x# and #3x-11# According to the question, #x+3x-11=69# #4x-11=69# #4x=69+11# #4x=80# #x=80/4# #color(magenta)(x=20# ~Hope this helps! :)

Eva Adamson · Answer

20 and 49

Let's have the smaller number be represented by a variable #x# and the larger number by #y#. Our first step is to create numerical equations that represent the numbers. The larger number is 11 less than the smaller number if the smaller number is multiplied by 3. Therefore, the first equation is: #y=3x-11#. Our second equation will be #x+y=69# since the sum is 69. Our next step is to substitute one equation into another. That way, we can form an equation with only one variable in it. Let's put our first equation into the second one: #x+(3x-11) = 69# From here, all we have to do is simplification: #x+3x-11=69# #4x-11=69# #4x=80# #x=20# We have our smaller number, #20#. To find the larger number, plug the smaller number into our second equation and solve for #y#: #20+y=69# #y=49# We now have our larger number #49#.

Savannah Anderson · Answer

The larger number is 49, and the smaller number is 20

It's easiest to make the questions into equations so that they are easier to understand. I'm going to abbreviate "larger number" to L and "smaller number" to S. When we see: The larger number is 11 less than 3 times the smaller number We can say: #L = 3S - 11# When we see: The sum is 69 We can say: #L + S = 69# Let's substitute the first equation into the second one. Since #L = 3S - 11#, we can put it into this equation: #L + S = 69# #(3S -11) + S = 69# #3S -11 + S = 69# #4S - 11 = 69# #4S = 80# #S = 20# Now that we know #S#, we can put it into the second equation. #L + S = 69# #L + 20 = 69# #L = 49# CHECK: #L = 3S - 11# #49 = 3(20) - 11# #49 = 60 - 11# #49=49# True. We know that our answers are correct.

Ethan Adkins · Answer

undefined Let the smaller number be x and the larger number be y.
According to the given conditions:
1. y = 3x - 11
2. x + y = 69
Substitute the value of y from equation 1 into equation 2:
x + (3x - 11) = 69
Combine like terms:
4x - 11 = 69
Add 11 to both sides:
4x = 80
Divide both sides by 4:
x = 20
Now, substitute the value of x into equation 1 to find y:
y = 3(20) - 11
y = 60 - 11
y = 49
So, the smaller number is 20 and the larger number is 49.