She can buy maximum of [tex]5[/tex] packages while staying within her budget.
Minimum spending limit [tex]=[/tex] $[tex]50[/tex].
Maximum spending limit [tex]=[/tex] $[tex]60[/tex].
Cost of one package of beads [tex]=[/tex] $[tex]4.95[/tex].
Number of packages of beads bought [tex]= 5[/tex].
Cost of one package of charms [tex]=[/tex] $[tex]6.55[/tex].
Let the number of packages of beads bought be [tex]x[/tex].
[tex]4.956 \times 5 + x \times 6.55 \geq 50[/tex]
[tex]24.78+6.55x\geq 50[/tex]
[tex]6.55x\geq 25.22[/tex]
[tex]x\geq 3.85[/tex]
[tex]4.956 \times 5 + x \times 6.55 \leq 60[/tex]
[tex]24.78+6.55x\leq 60[/tex]
[tex]6.55x\leq 35.22[/tex]
[tex]x\leq 5.38[/tex]
So, she can buy maximum of [tex]5[/tex] packages while staying within her budget.
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