The larger of two numbers is 18 more than 5 times the smaller. If 3 times the larger number is increased by 4 times the smaller, the result is 16. Find the numbers by solving algebraically
Oh, solving algebraically, you say? Well, I'll give it a try, but you know, numbers can be so serious sometimes. Let's see if we can lighten things up a little.
Let's call the smaller number "x" and the larger number "y". According to the clue, we know that:
y = 5x + 18 (Equation 1)
And we also know that:
3y + 4x = 16 (Equation 2)
Now, let's try to find a way to get these two equations to play nicely with each other.
First, let's rearrange Equation 2 a bit:
3y + 4x = 16
4x + 3y = 16 (Equation 3)
Now, let's use Equation 1 to substitute the value of "y" into Equation 3:
4x + 3(5x + 18) = 16 (Substituting y = 5x + 18)
Simplifying that equation:
4x + 15x + 54 = 16
19x + 54 = 16
Uh-oh! Our numbers are getting really serious here. We need to do some clown magic to make them smile again.
Let's subtract 54 from both sides:
19x = 16 - 54
19x = -38
Now, let's divide both sides by 19 to solve for x:
x = -38 / 19
x = -2
Okay, let's see if we can make the larger number laugh now. We'll substitute x = -2 into Equation 1:
y = 5x + 18
y = 5(-2) + 18
y = -10 + 18
y = 8
So, the smaller number is -2 and the larger number is 8.
There you have it! Solve algebraically, and the joke's on the numbers.
Step 1: Let's assume the smaller number as x and the larger number as y.
Step 2: According to the given information, we can write the following two equations:
Equation 1: y = 5x + 18 (The larger number is 18 more than 5 times the smaller)
Equation 2: 3y + 4x = 16 (3 times the larger number increased by 4 times the smaller is 16)
Step 3: Now, we will solve these equations simultaneously to find the values of x and y.
From Equation 1, we can express y in terms of x:
y = 5x + 18
Substitute this value of y in Equation 2:
3(5x + 18) + 4x = 16
Step 4: Distribute 3 to each term inside the parenthesis:
15x + 54 + 4x = 16
Step 5: Combine like terms:
19x + 54 = 16
Step 6: Move 54 to the other side:
19x = 16 - 54
19x = -38
Step 7: Divide both sides by 19 to isolate x:
x = -38/19
x = -2
Step 8: Substitute the value of x in Equation 1 to find y:
y = 5(-2) + 18
y = -10 + 18
y = 8
Step 9: Therefore, the smaller number is -2 and the larger number is 8.
To solve this problem algebraically, let's represent the smaller number as "x" and the larger number as "y."
From the given information, we can establish two equations:
1) The larger number is 18 more than 5 times the smaller:
y = 5x + 18
2) If 3 times the larger number is increased by 4 times the smaller, the result is 16:
3y + 4x = 16
To find the values of x and y, we can use a method called substitution. We will solve equation 1 for y and substitute that value into equation 2.
From equation 1, we have y = 5x + 18. Substitute this value of y into equation 2:
3(5x + 18) + 4x = 16
15x + 54 + 4x = 16
19x + 54 = 16
19x = 16 - 54
19x = -38
x = -38 / 19
x = -2
Now that we have found x, we can substitute it back into equation 1 to find y:
y = 5(-2) + 18
y = -10 + 18
y = 8
Therefore, the smaller number is -2 and the larger number is 8.
so put the words into math.
4x + 3(5x+18) = 16