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UKMT Senior Kangaroo, 2023

Algebra Difficulty 2.0 Junior Prove it United Kingdom

The smallest four two-digit primes are written in different squares of a $2 \times 2$ table. The sums of the numbers in each row and column are calculated. Two of these sums are $24$ and $28$ . The other two sums are $c$ and $d$ , where $c < d$ . What is the value of $5c + 7d$ ?

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