Dee bought 6 dolls and 2 toy trains for $55. At the same prices, Joy bought 4 dolls and 7 toy trains for $65. What is the price of a doll?

The price of a doll=$7.5

Step-by-step explanation:

Step 1: Express Dee's total cost

Dee's total cost can be expressed as;

Total cost = (price per doll*number of dolls bought) + (price per toy train*number of toy trains bought)

where;

Price per doll=d

number of dolls bought=6

Price per toy train=t

number of toy trains bought=2

Dee's total cost=$55

Replacing;

55 = (6*d) + (2*t)

6d+2t=55 ... equation 1

Step 2: Express Joy's total cost

Joy's total cost can be expressed as;

Total cost = (price per doll*number of dolls bought) + (price per toy train*number of toy trains bought)

where;

Price per doll=d

number of dolls bought=4

Price per toy train=t

number of toy trains bought=7

Dee's total cost=$65

Replacing;

65 = (4*d) + (7*t)

4d+7t=65 ... equation 2

Step: Solve simultaneously equation 1 and 2

4 (6d+2t=55) >>>24d+8t=220

-

6 (4d+7t=65) >>>24d+42t=390

(24d-24d) + (8t-42t) = 220-390

-34t=-170

t=-170/-34

t=5

Replace the value of t in equation 1;

6d+2t=55, t=5

6d + (2*5) = 55

6d+10=55

6d=55-10

6d=45

d=45/6

d=7.5

The price of a doll=$7.5