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Bright primary school Mathematics Competition
1。 Bright primary school sixth grade held a math contest with ***20 questions. Answer a question correctly and get 5 points; If you don't do 0 points, you will get 2 points if you make a mistake once. Jun Jun got 76 points, and he did as many wrong questions as he didn't. How many questions did he answer correctly?

He made as many mistakes as he didn't, but was deducted 1 point for making one mistake.

Assuming that he got all 20 questions correctly, 20 points will be deducted, which is 76+20=96 points different from the actual 76 points.

If the difference between doing right and doing wrong is 5+ 1=6, then he did right 96÷6= 16 and did wrong (20- 16)÷2=2, but didn't do 2.

2。 Spiders have eight legs, dragonflies have six legs and two pairs of wings, and cicadas have six legs and a pair of wings. At present, there are 20 of these three insects, 128 legs and 22 pairs of wings. How many of each?

Suppose all 20 are spiders, with 20×8= 160 legs, which is more than the actual 128 legs 160- 128 = 32 legs.

Spiders have 8-6=2 more legs than dragonflies (or cicadas), so there are 32÷2= 16 dragonflies and cicadas.

There are 20- 16=4 spiders.

Suppose 16 are all dragonflies with 16×2=32 pairs of wings, which is 32-22= 10 more than the actual 22 pairs.

Dragonflies have 2- 1= 1 wings more than cicadas.

10 The pair of wings should be 10÷ 1= 10 cicada.

There are 16- 10=6 dragonflies.

So, there are four spiders, six dragonflies and 10 cicadas.