Question

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Answer 1

`No.\ of\ Math\ Problems=26\\\ No.\ of\ Science\ Problems=16`

Explanation:

`In\ order\ to\ construct\ equations,\ we\ need\ to\ set\ variables.\\Hence,\\Let\ the\ no.\ of\ Math\ problems\ be\ x\\Let\ the\ no.\ of\ Science\ problems\ be\ y\\We\ are\ given\ that,\\No.\ of\ Math\ problems\ +No.\ of\ Science\ problems\ =42\\Hence,\\x+y=42\\We\ are\ also\ given,\\No.\ of\ Math\ problems\ =No.\ of\ Science\ problems\ +10\\Hence,\\x=y+10\\By\ transposing\ y\ to\ the\ LHS,\\x-y=10\\Now\ by\ gathering\ up\ our\ equations\ we\ can\ finally\ construct\ a\ system.\\Hence,\\`

`x+y=42\\x-y=10\\By\ simply\ adding\ the\ equations\ we\ get,\\(x+y)+(x-y)=42+10\\2x=52\\x=26\\Hence,\\Substituting\ x=26\ in\ Equation\ 1,\\26+y=42\\y=42-26\\y=16`

`Ultimately,\\No.\ of\ Math\ Problems=x=26\\\ No.\ of\ Science\ Problems=y=16`