Question

evan has 50 minutes of free time. evan wants to use this free time to make puppets and bead bracelets. he needs this much free time for each:
1 puppet \t10 minutes
1 bead bracelet\t10 minutes
click to select how many puppets and bead bracelets evan can make. you can choose any combination that uses up all of his free time.

Explanation:

Step1: Define variables

Let \( x \) be the number of puppets and \( y \) be the number of bead bracelets. The total time equation is \( 10x + 10y = 50 \). Simplify by dividing by 10: \( x + y = 5 \).

Step2: Find integer solutions

We can find pairs \((x,y)\) that satisfy \( x + y = 5 \). For example, if \( x = 2 \), then \( y = 5 - 2 = 3 \); if \( x = 3 \), \( y = 2 \); etc. A simple solution: let \( x = 2 \) (puppets) and \( y = 3 \) (bracelets), check \( 10(2)+10(3)=20 + 30 = 50 \), which works. Or \( x = 1 \), \( y = 4 \) (10+40=50), etc. One valid combination is 2 puppets and 3 bead bracelets (or other combinations like 1 and 4, 3 and 2, 4 and 1, 5 and 0, 0 and 5).

Answer:

One possible answer is 2 puppets and 3 bead bracelets (other valid combinations include 1 puppet and 4 bead bracelets, 3 puppets and 2 bead bracelets, 4 puppets and 1 bead bracelet, 5 puppets and 0 bead bracelets, 0 puppets and 5 bead bracelets).