We need to find 2 digit numbers (10-99) each of which has a) 8 divisors b) 9 divisors
Here's what I found: For 8 divisors, the number must have a. 3 distinct prime factors, or b. of the form {p^3, q} which are: 2^3*3=24 (1,2,3,4,6,8,12,24) 2*3*5=30 (1,2,3,5,6,10,15,30) 2^3*5=40 (1,2,4,5,8,10,20,40) 2*3*7=42 (1,2,3,6,7,14,21,42) 2*3^3=54 (1,2,3,6,9,18,27,54) 2^3*7=56 (1,2,4,7,8,14,28,56) 2*3*11=66 (1,2,3,6,11,22,33,66) 2^3*11=88 (1,2,4,8,11,22,44,88) 2*3*13=78 (1,2,3,6,13,26,39,78) 2*5*7=70 (1,2,5,7,10,14,35,70)
For 9 divisors, it is necessary that the 2-digit number be a perfect square, and the square-root is composite. For this, we can list only (2*3)^2=36 (1,2,3,4,6,9,12,18,36)
So there are 10 2-digit numbers with 8 factors, and 1 with 9 factors.
Note: looks like 72 has 12, the most factors in two digit numbers: 72 (1,2,3,4,6.8,9,12,18,24,36,72)
The cost of 1 vanilla ice cream and 1 strawberry ice cream should total to $31. Since you only bought one of each flavor, you simply have to add their unit prices.
Cost for 1 carton of strawberry ice cream + Cost for 1 carton of vanilla ice cream = Total Cost Total Cost = s + v --> this is the general equation
Since s = 1.5 + v, the modified equation would be Total Cost = 1.5 + v + v Total Cost = 1.5 + 2v
To factor quadratic equations of the form ax^2+bx+c=y, you must find two values, j and k, which satisfy two conditions.
jk=ac and j+k=b
The you replace the single linear term bx with jx and kx. Finally then you factor the first pair of terms and the second pair of terms. In this problem...
Well, this is a function. In order to solve this, you need a v value. Once you get a v value, you can plug into into 6+v^2 and wala- you get your answer.
