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Core examination paper from primary school to junior high school (mathematics)
First question

Let the number of fifth-grade students be A and the number of sixth-grade students be (324-a).

According to the meaning of the question, the number of boys in grade five is 5/9a, while that in grade six is 4/9(324-a).

Then the number of girls in grade five is 4/9a, and the number of girls in grade six is 5/9(324-a).

The number of girls is the same, that is, 4/9a =5/9(324-a).

Solution a= 180 (fifth grade) The number of sixth-grade students is 324- 180= 144.

the second question

If the Metasequoia tree is X, the Ginkgo tree is (18+x).

According to the meaning, the survival tree of Metasequoia glyptostroboides is X, and the survival tree of Ginkgo biloba is 95%( 18+x).

Column equation x+95%( 18+x)=60.

The number of trees with x=22 (Metasequoia glyptostroboides) is 22+ 18=40.

Third question

Let's say that Zhang's speed is 3a, Wang's speed is 2a, and the distance between the two villages is x kilometers.

According to the meaning of the question, when Zhang travels 1 1 km, the remaining distance is (x- 1 1) km, and the remaining distance is (x- 1 1)/3a.

Then Wang reached the finish line and walked (x- 1 1)/3a*2a kilometers, plus the original 5.5 kilometers.

It is 5/8 of the total distance.

Enumerable equation: 5.5+(x-11)/3a * 2a = 5/8.

Solution: X=44

The fourth question

One two three

Let the number of the original three piles of oranges be a b c.

Take out the second pile (a-b) 2b c from the first pile.

Take out the third pile (a-b) (2b-c) 2c from the second pile.

Take out the first pile 2(a-b) (2b-c) 2c-(a-b) from the third pile.

Sequence equation: 2 (a-b) =162b-c =162c-(a-b) =16.

Solution: a =18 b =10 c =16.