Q:

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?

Accepted Solution

A:
Answer:The price of a doll=$7.5Step-by-step explanation:Step 1: Express Dee's total costDee'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=dnumber of dolls bought=6Price per toy train=tnumber of toy trains bought=2Dee's total cost=$55Replacing;55=(6×d)+(2×t)6d+2t=55...equation 1Step 2: Express Joy's total costJoy'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=dnumber of dolls bought=4Price per toy train=tnumber of toy trains bought=7Dee's total cost=$65Replacing;65=(4×d)+(7×t)4d+7t=65...equation 2Step: Solve simultaneously equation 1 and 24(6d+2t=55)>>>24d+8t=220-6(4d+7t=65)>>>24d+42t=390(24d-24d)+(8t-42t)=220-390-34t=-170t=-170/-34t=5Replace the value of t in equation 1;6d+2t=55, t=56d+(2×5)=556d+10=556d=55-106d=45d=45/6d=7.5The price of a doll=$7.5