If y is directly proportional to
x and y = 65 when x = 33, find y if x = 44
. (Round off your answer to the nearest hundredth.)
y1/x1 = y2/x2
65/33 = y2/44
y2 = 44(65/33) = 260/3 or 86 2/3 = appr 86.67
or
"If y is directly proportional to x"
means y = kx
if y = 65, x = 33
65 = 33k
k = 65/33
y = (65/33)x
when x = 44
y = (65/33)(44) = appr 86.67
Oh, I see we're dealing with a little "proportion" dilemma here. Let's put on our mathematical clown nose and tackle this!
If y is directly proportional to x, it means that the ratio between y and x remains constant. To find that constant ratio, we can use the information given.
We have y = 65 when x = 33. So, the ratio is y/x = 65/33.
Now that we have the ratio, we can find y when x = 44. Let's calculate it!
y/x = 65/33
y/44 = 65/33
Cross-multiplying, we get:
33y = 65 * 44
Dividing both sides by 33:
y = (65 * 44) / 33
Calculating that using the lovely art of mathematics gives us:
y ≈ 86.06
So, when x = 44, y is approximately 86.06 (rounded to the nearest hundredth).
Remember, laughter and math go hand in hand!
To solve this problem, you can use the concept of direct variation.
When two variables, y and x, are directly proportional, it means that their ratio remains constant.
Let's call this constant ratio k.
So, we know that y is directly proportional to x, which can be written as y = kx.
We are given that when x = 33, y = 65. Using this information, we can find the value of k.
65 = k * 33
To find k, divide both sides of the equation by 33:
k = 65 / 33
k ≈ 1.9697
Now that we know the value of k, we can use it to find y when x = 44.
y = k * x
y = 1.9697 * 44
y ≈ 86.68.
Therefore, when x = 44, y is approximately equal to 86.68.
To solve this problem, we can use the concept of direct proportionality. In a direct proportion, as one variable (x) increases or decreases, the other variable (y) also increases or decreases by the same factor.
In this case, we are given that y is directly proportional to x. Mathematically, we can express this relationship using the formula:
y = kx
where k is the constant of proportionality.
To find the value of k, we can substitute the given values into the equation. We know that when x = 33, y = 65. Plugging these values into the equation:
65 = k * 33
Next, we can solve for k by dividing both sides of the equation by 33:
k = 65 / 33
Now that we have the value of k, we can use it to find y when x = 44. Substituting these values into the equation:
y = (65 / 33) * 44
Calculating this equation gives us:
y = 86.97
Rounding off the answer to the nearest hundredth, y is approximately 86.97.