MANUFACTURING A shoe manufacturer spends 2.50 to make sandals and 4 to make running shoes During a typical month they spend 2500 manufacturing sandals and running shoes. During the month of April, they double the pairs of sandais manufactured and spend a total of 3000. How many pairs of sandals and running shoes does the company make during a typical month? Number of sandals: square Number of running shoes: square

Let's denote the number of pairs of sandals made during a typical month as $s$ and the number of pairs of running shoes made as $r$.<br /><br />We are given the following information:<br /><br />1. The cost to make sandals is $\$2.50$ each.<br />2. The cost to make running shoes is $\$4$ each.<br />3. During a typical month, the company spends $\$2500$ manufacturing sandals and running shoes.<br />4. During the month of April, the company doubles the number of pairs of sandals manufactured and spends a total of $\$3000$.<br /><br />We can set up a system of equations based on this information:<br /><br />For a typical month:<br />\[2.50s + 4r = 2500\]<br /><br />For the month of April, where the number of pairs of sandals is doubled:<br />\[2.50(2s) + 4r3000\]<br /><br />Now, let's solve this system of equations step by step.<br /><br />First, simplify the second equation:<br />\[5s + 4r = 3000\]<br /><br />Now we have two equations:<br />\[2.50s + 4r = 2500\]<br />\[5s + 4r = 3000\]<br /><br />To eliminate $r$, we can multiply the first equation by 2:<br />\[5s + 8r = 5000\]<br /><br />Now subtract the second equation from this new equation:<br />\[5s + 8r - (5s + 4r) = 5000 - 3000\]<br />\[4r = 2000\]<br />\[r = 500\]<br /><br />Now that we have the value of $r$, we can substitute it back into one of the original equations to find $s$. Let's use the first equation:<br />\[2.50s + 4(500) = 2500\]<br />\[2.50s + 2000 = 2500\]<br />\[2.50s = 500\]<br />\[s = 200\]<br /><br />Therefore, during a typical month, the company makes:<br />Number of sandals: $\boxed{200}$<br />Number of running shoes: $\boxed{500}$