(total number of feet-number of feet per chicken × total number of heads) ÷ (number of feet per rabbit-number of feet per chicken) = number of rabbits;
Total number of rabbits = number of chickens.
Or (number of feet per rabbit × total head-total feet) ÷ (number of feet per rabbit-number of feet per chicken) = number of chickens;
Total number of chickens = rabbits.
For example, "Thirty-six chickens and rabbits, enough 100. How many chickens and rabbits are there? "
Solution1(100-2× 36) ÷ (4-2) =14 (only)
36- 14=22 (chicken only).
Solution 2 (4×36- 100)÷(4-2)=22 (only) ............................................................................................................................
36-22= 14 (......................... rabbit only).
2) Given the difference between the total number of chickens and rabbits, when the total number of chickens is greater than that of rabbits, the formula can be used.
(number of feet per chicken × total head-foot difference) ÷ (number of feet per chicken+number of feet per rabbit) = number of rabbits;
Total number of rabbits = number of chickens
Or (the number of feet per rabbit × the total number of heads+the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet exempted from each chicken) = the number of chickens;
Total number of chickens = rabbits. (Example omitted)
(3) Given the difference between the total number of feet of chickens and rabbits, when the total number of feet of rabbits is greater than that of chickens, the formula can be used.
(the number of feet per chicken × the total number of heads+the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet per rabbit) = the number of rabbits;
Total number of rabbits = number of chickens.
Or (the number of feet per rabbit × the total number of heads-the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet per rabbit) = the number of chickens;
(4) The following formula can be used to solve the gain and loss problem (the generalization of the chicken-rabbit problem):
(65438 points +0 number of qualified products × total number of products-total score obtained) ÷ (score of each qualified product+deduction of each unqualified product) = number of unqualified products. Or total number of products-(points deducted for each unqualified product × total number of products+total score obtained) ÷ (points deducted for each qualified product+points deducted for each unqualified product) = number of unqualified products.
For example, "the workers who produce light bulbs in the light bulb factory are paid by points." Each qualified product will get 4 points, while each unqualified product will not be scored, and 15 points will be deducted. A worker produced 1000 light bulbs, and * * * got 3525 points. How many of them are unqualified? "
Solution1(4×1000-3525) ÷ (4+15)
=475÷ 19=25 (pieces)
Solution 21000-(15×1000+3525) ÷ (4+15)
= 1000- 18525÷ 19
= 1000-975=25 (pieces) (omitted)
("the gain and loss problem" is also called "the problem of handling glassware". If the glassware is transported intact, the freight is RMB. })
5) The problem of chicken-rabbit exchange (the problem of finding the number of chickens and rabbits after knowing the total number of feet and the total number of feet after chicken-rabbit exchange) can be solved by the following formula:
[(sum of total feet twice) ÷ (sum of feet of each chicken and rabbit)+(difference of total feet twice) ÷ (difference of feet of each chicken and rabbit) ÷ 2 = number of chickens;
⊙ (sum of total feet twice) ⊙ (sum of feet of each chicken and rabbit)-(difference of total feet twice) ⊙ (difference of feet of each chicken and rabbit) ⊙2 = number of rabbits.
For example, "There are some chickens and rabbits, and * * * has 44 feet. If the number of chickens and rabbits is reversed, * * * has 52 feet. How many chickens and rabbits are there? "
Solution [(52+44) ÷ (4+2)+(52-44) ÷ (4-2)] ÷ 2
=20÷2= 10 (only applicable)
〔(52+44)÷(4+2)-(52-44)÷(4-2)〕÷2
= 12÷2=6 (only applicable)
Total number of chickens = rabbits. (Example omitted)