If y varies directly as X and X=88 when Y= 110, find X whaen Y=70

Set up a proportion:
88/110 = X/70. solve for X.

To solve this problem, we use the concept of direct variation. In direct variation, if one variable (Y) varies directly as another variable (X), it means that as X increases or decreases, Y also increases or decreases by the same factor.

In this case, we are given that Y varies directly as X. This can be expressed mathematically as Y = kX, where k is the constant of variation.

We are also given that when X = 88, Y = 110. Using this information, we can find the value of k. Plugging in the values into the equation, we have 110 = k * 88.

To solve for k, divide both sides of the equation by 88. 110/88 = k. Simplifying the equation, we get k ≈ 1.25.

Now that we have the value of k, we can use it to find X when Y = 70. We set up a proportion using the equation Y = kX, giving us 88/110 = X/70.

To solve for X, we cross-multiply and then divide. 88 * 70 = 110X. Simplifying the equation gives us 6160 = 110X.

Finally, we divide both sides of the equation by 110 to isolate X. 6160/110 ≈ 56.

Therefore, when Y = 70, X is approximately equal to 56.