The difference between two positive numbers is 9. If four times the larger number is ten times the smaller number, what is the larger number?
smaller --- x
larger ---- x+9
4(x+9) = 10x
solve for x
Well, well, well, we have a mathematical mystery on our hands! Let's put on our detective hats and solve it with a touch of humor, shall we?
Let's call the larger number "L" and the smaller number "S". According to our mystery clues, we have two hints to unravel this riddle.
First, we know that the difference between the two positive numbers is 9. So, we can say: L - S = 9.
Now, the second clue is that four times the larger number is ten times the smaller number. In mathematical terms, we can express this as: 4L = 10S.
Here's where the fun begins! We'll use our cunning deduction skills to figure out the larger number.
From the first clue, we can rewrite the equation as L = S + 9. Now, you've probably noticed that we have two expressions for "L". Let's substitute the second expression into the second clue equation.
4(S + 9) = 10S
Now, let's put our math skills to good use and solve for "S".
Expand the equation:
4S + 36 = 10S
Subtract 4S from both sides:
36 = 6S
Finally, divide both sides by 6:
S = 6
Voila! We've discovered that the smaller number is 6. But wait, our quest is not over yet! Let's find the larger number.
Using the equation L = S + 9 and substituting the value of S, we have:
L = 6 + 9
L = 15
Huzzah! The larger number is 15. Our mathematical mystery has been solved, thanks to a touch of humor and some crafty deduction!
Keep those brain teasers coming, I'm all ears for more puzzling problems!
Let's solve this step by step:
Let's assume the two positive numbers are x and y, where x is the larger number.
According to the given information:
1) The difference between the two positive numbers is 9:
x - y = 9 (Equation 1)
2) Four times the larger number is ten times the smaller number:
4x = 10y (Equation 2)
We can solve this system of equations to find the value of x, which is the larger number.
Step 1: Solve Equation 1 for x:
x = y + 9
Step 2: Substitute the value of x from Step 1 into Equation 2:
4(y + 9) = 10y
Step 3: Expand and simplify:
4y + 36 = 10y
Step 4: Subtract 4y from both sides:
36 = 6y
Step 5: Divide both sides by 6 to solve for y:
y = 6
Step 6: Substitute the value of y into Equation 1 to solve for x:
x = 6 + 9
x = 15
Therefore, the larger number is 15.
To solve this problem, we can use algebraic expressions. Let's assume the larger number as 'x' and the smaller number as 'y'.
According to the problem, we are given two conditions:
1. The difference between the two positive numbers is 9: x - y = 9
2. Four times the larger number is ten times the smaller number: 4x = 10y
From the first condition, we can rewrite it as x = y + 9.
Substituting this value in the second condition:
4(y + 9) = 10y
Now, let's simplify the equation step-by-step:
4y + 36 = 10y
36 = 10y - 4y
36 = 6y
Finally, divide both sides of the equation by 6:
y = 6
So, the smaller number is 6.
To find the larger number, substitute the smaller number back into one of the initial equations. Let's use x = y + 9:
x = 6 + 9
x = 15
Therefore, the larger number is 15.
In conclusion, the larger number is 15.