Corey had 1 3/4 as many sports cards as Miguel. When Miguel gave half of his sports cards to Corey, he then had 18 fewer sports cards than his friend. How many sports cards did Miguel have at first?
+313 To calculate
the number of sports cards Miguel had.
Let y be the initial Corey's sports cards and x be the initial Miguel's sports cards then according to the question we have,
⇒ Initial Corey's sports cards= (\(1 {3 \over 4}{}{}\)) (Initial Miguel's sports cards)
⇒ y = (\( {7 \over 4}{}{}\))(x)
⇒ y =\({7x \over 4}{}{}\)
After giving half of Miguel's sports cards to his friend, Miguel's final sports cards are
\(x\)-\( {x \over 2}{}{}\) and Corey's sports card are \(y\)+\( {x \over 2}{}{}\).
According to the question,
⇒ Final Miguel's sports cards=(Final Corey's sports cards)−18
⇒ (x - \({x\over 2}{}{}\)) = (y + \( {x \over 2}{}{}\)) - 18
⇒ \(y\) = 18
Plug it above,
⇒ 18 = \( {7x \over 4}{}{}\)
⇒ \(x\) = \({18 * 4\over 7}{}{}\)
⇒ \(x\) = 10.29
⇒ \(x\) = 10
Thus, Miguel had 10 sports cards at first.
