There are 66 purple marbles in the bag.
Step-by-step explanation:
Given,
Total number of marbles in bag = 82
Let,
Number of purple marbles = x
Number of white marbles = y
According to given statement;
x+y=82 Eqn 1
The number of purple marble is 2 more than 4 times the number of white marbles.
x=4y+2 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](4y+2)+y=82\\4y+2+y=82\\5y=82-2\\5y=80[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{80}{5}\\y=16[/tex]
Putting y=16 in Eqn 2
[tex]x=4(16)+2\\x=64+2\\x=66[/tex]
There are 66 purple marbles in the bag.
Keywords: linear equation, variable
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