The sum of two integers is greater than 12. One integer is ten less than twice the other. What are the least values of the integer?
how would you set up this problem???
The sum of two integers is greater than 12. One integer is ten less than twice the other. What are the least values of the integer?
how would you set up this problem???
a + b = 12+
a = 2b - 10
a + 10 = 2b
a + b = 12+
10 - b = 20 - 12+
3b = 22+
Minimum b = 8
Corresponding minimum a = 6
6 = 2(8) - 10
Well, let's give it a shot! Let's call one of the integers "x" and the other "y". We can set up two equations based on the given information:
1) x + y > 12 (the sum of the two integers is greater than 12)
2) x = 2y - 10 (one integer is ten less than twice the other)
Now, we can use these equations to find the least values of the integers. But remember, I'm here to bring the laughs, not just provide the answer! So, let's see if we can clown around with the numbers a bit:
Since it says one integer is ten less than twice the other, let's start by assuming that y is the larger integer. If y is the larger integer, then x (being ten less than twice y) must be even smaller. So, let's assume y = 5 (since it's greater than 12) and try to find x:
x = 2(5) - 10
x = 0
Oops! We ended up with x = 0, which is less than 12. So, it seems our assumption was wrong. Let's switch things up and assume that x is the larger integer this time.
If x is larger, then y (being ten less than twice x) must be even smaller. So, let's assume x = 10 (since it's greater than 12) and try to find y:
y = 2(10) - 10
y = 10
Great! This time we got y = 10, which is indeed greater than 12. Now let's plug these values back into the first equation to check:
x + y = 10 + 10 = 20
Well, well, well! The sum of x and y is indeed greater than 12. So, the least values of the integers in this scenario would be x = 10 and y = 10.
Remember, though, there could be different valid combinations of x and y that satisfy the given conditions. So don't forget to explore other possibilities too!
To set up this problem, you need to assign variables to the two integers. Let's call one integer "x" and the other "y".
Given that "the sum of two integers is greater than 12," we can write an inequality as: x + y > 12.
Now, we are also given that "one integer is ten less than twice the other." This can be expressed as an equation: x = 2y - 10.
Now you have a system of equations:
x + y > 12
x = 2y - 10
To find the least values of the integers, we need to solve this system of equations.