Answer:
Joyce has total 62 colored beads.
Step-by-step explanation:
For making groups of 9, let the number of beads be x.
total beads = 9x + 8
For making groups of 8, let the number of beads be y.
total beads = 8y + 6
As the total number of beads in both cases are same so,
9x + 8= 8y + 6
or, 9x-8y = -2
Now lets check the values through hit and trial;
First check; x=6, y=7
9*6 - 8*7 = -2
or, 54- 56 = -2
or, -2 =-2
This satisfies our equation.
Hence; Total beads = 9*6 + 8 = 62
The total number of beads joyce had is 62.
Number of beads she have is 62 .
Step-by-step explanation:
Here we have , joyce has between 25 to 75 colored beads. when she makes them into groups of 9, 8 beads are left out. when she groups into groups of 8, We need to find how many beads are left . Let's solve this:
when she makes them into groups of 9, 8 beads are left out equation is
[tex]9x+8[/tex]
when she groups into groups of 8 , 6 beads are left out, equation is
[tex]8y+6[/tex]
Equating both equation's we get:
⇒ [tex]9x+8 = 8y+6[/tex]
⇒ [tex]9x-8y = -2[/tex]
By hit & trial method , we put x = 6 & y=7:
⇒ [tex]9(6)-8(7) = -2[/tex]
⇒ [tex]54-56= -2[/tex]
⇒ [tex]-2= -2[/tex]
Since , LHS = RHS x = 6 & y=7 satisfies the equation [tex]9x+8 = 8y+6[/tex] . So putting value of x=6 in [tex]9x+8[/tex] we get:
⇒ [tex]9x+8[/tex]
⇒ [tex]54+8[/tex]
⇒ [tex]62[/tex]
Therefore, Number of beads she have is 62 .
