A bag contains purple marbles and white marbles, 111 in total. The number of purple marbles is 9 more than 5 times the number of white marbles. How many purple marbles are there?

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absor201 absor201 · Answer 1 · 2019-11-07T18:42:59+01:00

The number of purple marbles is 94.

Further explanation:

Let w be the number of white marbles

and

p be the number of purple marbles

Then

[tex]w+p = 111[/tex]

and

p = 5w+9

Putting p=5w+9 in first equation

[tex]w+(5w+9)=11\\w+5w+9=111\\6w+9=111[/tex]

Subtracting 9 from both sides

[tex]6w+9-9=111-9\\6w=102[/tex]

Dividing both sides by 6

[tex]\frac{6w}{6}=\frac{102}{6}\\ w=17[/tex]

Putting w=17 in p=5w+9

[tex]p=5(17)+9\\=85+9\\=94[/tex]

The number of purple marbles is 94.

Keywords: Linear equations, Word problems

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