40 points for this algebra word problem

9

Step-by-step explanation:

let the number

=

x

then 4 times the number

=

4

x

and 4 times the number increased by 15

=

4

x

+

15

also 6 times the number

=

6

x

and 3 less than 6 times the number

=

6

x

−

3

equating the two expressions gives the equation

4

x

+

15

=

6

x

−

3

←

solve for x

subtract 6x from both sides

4

x

−

6

x

+

15

=

6

x

−

6

x

−

3

⇒

−

2

x

+

15

=

−

3

subtract 15 from both sides

−

2

x

+

15

−

15

=

−

3

−

15

⇒

−

2

x

=

−

18

divide both sides by

−

2

−

2

x

−

2

=

−

18

−

2

⇒

x

=

9

As a check

(

4

×

9

)

+

15

=

36

+

15

=

51

(

6

×

9

)

−

3

=

54

−

3

=

51

⇒

the number is 9

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.