Need help with problem

Question

I need help with a maths problem I'm doing during homeschooling. If you could give me a hint as to how to work it out without giving the answer, that would be fantastic. Thank you.

Sam has two cards. Each card has a number on the front and a different number on the back. The numbers on the front of the cards are 26 + 30 = 56.

Sam puts the cards down so that he can see one of the numbers on each card. He does this several times, sometimes turning over one or both cards. He works out the total of the numbers each time and gets four different totals: 51, 53, 56 and 58.

What are the numbers on the back of the cards?

Answer 1

51, 53, 56, 58

26+30 = 56

26+X = either 51, 53 or 58, X is either 25, 27 or 32

30+Y = either 51, 53 or 58, Y is either 21, 23 or 28

X+Y = either 51, 53 or 58 X+Y = 25+28 or 32+21

X and Y are the reverse sides of 26 and 30

Y is 28 or 21, X is 25 or 32

the back of the cards are either 25 and 28 or 32 and 21

back of 30 is either 21 or 28, they sum to 51 or 58

back of 26 is either 25 or 32, they sum to 51 or 58

30+26 = 56

X+Y = 53 = 25+28 or 21+32

What numbers are on the back of the cards? Either 25 & 28, or 21 & 32