Let P= 1 cent coin and the number of pieces Diana brought.
N= the number of nickels and coins brought by Diana,
Q= Diana's number of coins and pieces,
T= the total amount of money Diana spent on candy (in cents),
A= number of sweets purchased for orsi Ya,
B= number of sweets purchased for Blyth,
C= the number of sweets bought for Carrie,
D= unit price (in cents) of souvenirs purchased by mother,
F= number of souvenirs purchased by mother.
The above figures are positive integers.
According to (1):(la)P+N+Q= 13,
( 1b)P+5N+25Q=T。
According to (2):(2)2a+3b+6c=T 。
According to (3): (3) A, B and C are different and are all greater than 1.
According to (4):(4) or 2a=3b, or 2a=6c or 3b=6c.
According to (5):(5)F×d=480.
According to (6): (6) A+B+C = F.
According to (7), the problem can be reformulated as:
(7) Which is the largest, A, B and C?
Here a * * * has six equations and nine unknowns, and the fourth equation is one of three possible equations. There are too many equations to be solved only by algebraic method, and we must look for other characteristics except that all numbers are positive integers.
We know that the sum of two odd numbers is always even,
The sum of two even numbers is always even,
The sum of odd and even numbers is always odd.
We know that the product of two odd numbers is always odd,
The product of two even numbers is always even,
The product of odd and even numbers is always even.
According to these laws, in the equation (1a), or P, N, Q N and Q are all odd numbers.
Number, or only one of these three numbers is odd. In either case, t in (1b) is always odd, so b in equation (2) is also odd. Therefore, in equation (4), 2a cannot be equal to 3b, because 2a is an even number and 3b is an odd number. 3b cannot be equal to 6c, because 6c is even and 3b is odd. Therefore,
Since B is odd, F is odd in B+4c = F. In Equation (5), 480 is the product of two numbers, one of which is odd (F) and the other is even (D). In this product, the only odd value f can take is l, 3, 5 or 15. F equals 65438+.
So b+4c= 15, and c cannot be greater than 3 or less than 1. According to (3), c cannot be equal to 1 or 3, otherwise b is equal to 3). So c must be equal to 2. So b=7. According to the previous a=3c, so a=6. So b is the largest number.
Other values can be solved as follows. Because F= 15, according to (5), D = 32. Because A = 6, B = 7, C = 2, according to (2), T = 45. Subtract from (1b)
(la) gives 4N+240=32. Divide the two sides by 4 to get N+6Q=8. Q cannot be greater than 1 (otherwise n is negative) or less than 1 (because according to (l), Diana has a quarter), so Q = L. So N=2.
In a word, Blyth is Diana's sister.
I am exhausted.