Machine A pack = 7200/p boxes of cookies
Machine B pack = 7200/p+2.60 boxes of cookies
Machine A can pack 1560 more boxes of cookies thanks machine B.
Form an equation which reduces to 1560p^2 + 4056p - 18720 = 0 and explain why is this equation is true.
angel m1 =125 dagrees
angek m2= ?
To form the equation, let's break down the problem step by step:
1. The first step is to determine the number of boxes of cookies packed by machine A. We are given that the number of boxes packed by machine A is given by 7200 divided by p.
2. The second step is to determine the number of boxes of cookies packed by machine B. We are given that the number of boxes packed by machine B is given by 7200 divided by p + 2.60.
3. Machine A can pack 1560 more boxes of cookies than machine B. This means that the number of boxes packed by machine A minus the number of boxes packed by machine B is equal to 1560. Mathematically, it can be represented as: (7200/p) - (7200/(p + 2.60)) = 1560.
4. To simplify the equation, we need to find a common denominator for the fractions. The common denominator is p(p + 2.60), so we can rewrite the equation as: (7200(p + 2.60) - 7200p) / (p(p + 2.60)) = 1560.
5. Simplifying the equation further, we have: (7200p + 18720 - 7200p) / (p(p + 2.60)) = 1560.
6. Simplifying the numerator gives us: 18720 / (p(p + 2.60)) = 1560.
7. To remove the fractions, we can multiply both sides of the equation by (p(p + 2.60)): 18720 = 1560(p(p + 2.60)).
8. Expanding the right-hand side gives us: 18720 = 1560p^2 + 4056p.
9. Rearranging the terms gives us the final equation: 1560p^2 + 4056p - 18720 = 0.
Therefore, the equation 1560p^2 + 4056p - 18720 = 0 is true because it represents the condition where machine A can pack 1560 more boxes of cookies than machine B.