To solve this problem, we need to establish the relationship between y and x based on the information given. When we say that y varies directly with x, it means that there is a constant of proportionality (k) such that:
y = k * x
We know from the problem that when x is 84, y is 252. We can use this information to find the value of k:
252 = k * 84
To find k, we divide both sides by 84:
k = 252 / 84
Calculating this gives:
k = 3
Now that we have the constant of proportionality (k), we can use it to find y when x is 74:
y = k * x
y = 3 * 74
Now, doing the calculation:
y = 222
So, when x is 74, the value of y is 222.