Question

How do you figure this out?

Answer 1

Let the money with Miguel be x.

Then :

Money with Kira = x - 9

Money with Charlie = 4x

Total money in their wallet = $105

This can be written in an equation as :

= \tt \: x + x - 9 + 4x = 105=x+x−9+4x=105

= \tt2x + 4x - 9 = 105=2x+4x−9=105

= \tt 6x - 9 = 105=6x−9=105

= \tt6x = 105 + 9=6x=105+9

= \tt6x = 114=6x=114

= \tt x = \frac{114}{6}=x=

6

114

= \tt x = 19=x=19

Which means :

Money with Miguel = $19

Money with Kira :

= 19 - 9

Thus, Kira has $10 in her wallet.

Money with Charlie :

= 4 × 19

= 76

Thus, Charlie has $76 in his wallet.

Therefore,

Money with Kira = $10

Money with Charlie = $76

Money with Miguel = $19

Answer 2

Let the red cat be represented by x.

Let the yellow cat be represented by y.

Let the white cat be represented by z.

Which means :

`\tt (1) \: (4)/(5) (20x - 5)`

`\tt = (4)/(5) * 20x - \frac {4 }{5} * 5`

`\tt= (80x)/(5) - (20)/(5)`

`\tt = 16x - 14`

Thus, the first statement is correct.

`\tt(2) \: (3)/(5) ( (1)/(3) z - 10)`

`\tt = (3)/(5) * (1)/(3) z - (3)/(5) * 10`

`\tt = (3)/(15) z- (30)/(5)`

`\tt = (1)/(5) z - 6`

Thus, the second statement is a lie.

`\tt(3) \: (1)/(9) ( - 9y - 27x)`

`\tt= (1)/(9) * - 9y - (1)/(9) * 27x`

`\tt = ( - 9)/( \: \: 9) y - (27)/(9) x`

`\tt = (- y) - 3x`

Thus, the third statement is correct.

Therefore, the second one is a lie.