2 integers are in a ratio of 5 : 8. If there sum is less than 100. What is the greatest possible valsue of the smallest interger
the two numbers are 5x and 8x
You need
5x+8x < 100
find the maximum value of x, and then you want 5x
Well, let's start by setting up the equation. Let's say the two integers are 5x and 8x (since their ratio is 5:8). Now we need to find the greatest possible value of the smallest integer, which is 5x.
Since the sum of the two integers is less than 100, we can write the equation as:
5x + 8x < 100
Combining like terms, we have:
13x < 100
To find the greatest possible value of x, we need to divide both sides of the equation by 13:
x < 100/13
Since x is an integer, the greatest possible value of x would be the largest integer less than 100/13, which is 7.
Now let's find the corresponding value for 5x by substituting x = 7 into the equation:
5x = 5 * 7 = 35
Therefore, the greatest possible value of the smallest integer is 35.
To find the greatest possible value of the smaller integer, we need to determine the ratio between the two integers.
Let's assume the smaller integer is 5x, and the larger integer is 8x, where x is a positive integer.
According to the given ratio, 5x : 8x, the smaller integer is 5/8 times the size of the larger integer.
Now, since their sum is less than 100, we can set up an inequality:
5x + 8x < 100
Combining like terms, we get:
13x < 100
Next, divide both sides of the inequality by 13:
x < 100/13
Since x must be a positive integer, we round down to the nearest whole number:
x = 7
Finally, we can find the greatest possible value of the smaller integer by substituting x = 7 back into the equation:
smaller integer = 5x = 5 * 7 = 35
Therefore, the greatest possible value of the smaller integer is 35.
To find the greatest possible value of the smallest integer, let's use a system of equations.
Let's assume the two integers are 5x and 8x, where x is a positive integer.
According to the given ratio, the two integers are in the ratio of 5:8, so we can set up the equation:
5x + 8x < 100
Combining like terms, we have:
13x < 100
To solve for x, divide both sides of the inequality by 13:
x < 100/13
Since x must be a positive integer, the greatest possible value of x is the largest integer less than 100/13, which is 7.
Therefore, the greatest possible value of the smallest integer is 5 * 7 = 35.