Final answer:
Saul and Javier would need to purchase 5 pairs of socks each for both of them to pay the same total amount.
Step-by-step explanation:
To find out how many pairs of socks Saul and Javier must buy for both to pay the same amount, we need to set up an equation where both parties' total cost will be equal. Saul's cost per pair is $7.50 with no additional shipping fee. In contrast, Javier has a cost per pair of $6.00 and an additional $7.50 shipping fee, no matter how many pairs he buys.
Let's use 'x' to represent the number of pairs both Saul and Javier will order. The total cost for Saul is then $7.50x, while the total cost for Javier is $6.00x + $7.50. By setting these two expressions as equal, we get the equation:
$7.50x = $6.00x + $7.50
To solve for 'x', we subtract $6.00x from both sides:
$7.50x - $6.00x = $7.50
Which simplifies to:
$1.50x = $7.50
Now, we simply divide both sides by $1.50 to find 'x':
$x = $7.50 / $1.50
$x = 5
So, Saul and Javier have to purchase 5 pairs of socks each for their total costs to be the same.