Call Ben's units B and Jerry's units J.

5B + 4J = 530 ①

Ben lost 4/5 of his cards and Jerry lost ¼ of his cards.

That's 4B and 1J.

Total cards lost = 530 - 370
= 160

So 4B + 1J = 160

Multiply this by 4,

4 x (4B + 1J) = 4 x 160
16B + 4J = 640 ②

Compare this to ①,

Difference = 16B - 5B = 11B
Difference also = 640 - 530 = 110

So 11B = 110

1B = 110 ÷ 11
1B = 10

Ben's cards at first
= 5B
= 5 x 10
= 50

Model :

At first :

Ben ⬛⬛⬛⬛⬛
Jerry☆☆☆☆
Total = 5⬛ + 4☆ = 530

Cards lost :

Ben ⬛⬛⬛⬛
Jerry ☆

530 - 370 = 160 = 4⬛ + 1☆

If 4⬛ + 1☆ = 160,

Then

⬛⬛⬛⬛ ☆ ⬛⬛⬛⬛ ☆⬛⬛⬛⬛ ☆ ⬛⬛⬛⬛ ☆

= 16⬛ + 4☆
= 160 x 4
= 640

640 - 530 = 110

= 16⬛ + 4☆ - 5⬛ - 4☆
= 11⬛

1⬛ = 110 ÷ 10
= 10

Ben's at first
= 5⬛
= 5 x 10
= 50

Many thanks

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