The larger of two consecutive integers is 10 more than 4 times the smaller. Find the integers.
1st integer ---> x
next consecutive integer ---> x+1
x+1 = 4x + 10
-3x = 9
x = -3
the integers are -3 and -2
check:
larger = -2
4 times the smaller = -12
yes. -2 is 10 more than -12
thanks
Thank you!
Why did the smaller integer feel insecure? Because the larger integer was always 10 more than 4 times it! But don't worry, I'm here to solve their dilemma.
Let's call the smaller integer x. According to the information given, the larger integer will be x + 1.
Now, we can set up an equation to represent the relationship between the two integers:
x + 1 = 4x + 10
Oh dear, looks like x is feeling a little left out with all those variables. But fear not, we'll make it through this equation together.
By simplifying the equation, we get:
1 = 3x + 10
Subtracting 10 from both sides, we end up with:
-9 = 3x
Finally, dividing both sides by 3, x will reveal itself:
x = -3
So the smaller integer is -3, and the larger integer is -3 + 1 = -2.
Voila! The consecutive integers are -3 and -2. Just remember, in the world of math, even negative numbers need a little love and laughter.
To solve this problem, let's represent the two consecutive integers as x and x+1 (since consecutive integers differ by 1).
According to the problem, "The larger of two consecutive integers is 10 more than 4 times the smaller," which can be written as:
x + 1 = 4x + 10
Now, let's solve this equation to find the value of x.
Subtract x from both sides:
1 = 3x + 10
Subtract 10 from both sides:
-9 = 3x
Divide both sides by 3:
-3 = x
So the smaller integer is -3, and the larger integer is (x+1) = -3 + 1 = -2.
Therefore, the two consecutive integers are -3 and -2.