Question

What can you figure out about the prices of the items (hat, pikachu, briefcase)? Show or explain your thinking.

Answer 1

Step 1

Write out the equations representing each slide in the problem

Let the hat be = x

The golden rabbit = y

The briefcase = z

Hence

5x + y +3z = $237 .......................(1)

7x+7z= $371 ..................................(2)

8x + 3y + z = $320 .................(3)

Step 2

Solve the equations by substitution of the value of z from equation (2) into equation (1) and (3)

From (2)

7z = 371 -7x

z = (371-7x)/7

Substituting this value into equation (1) and (3) gives

`\begin{gathered} 5x+y+3((371-7x)/(7))=237\ldots\ldots\ldots\ldots\ldots..\ldots..\mathrm{}(4) \\ 8x+3y\text{ +}(371-7x)/(7)=320\ldots.\ldots\ldots\ldots\ldots\ldots.\text{.}\mathrm{}(5) \end{gathered}`

Step 4

Find the value of x and y by elimination method

`35x+7y+3(371-7x)=1659`
`\begin{gathered} 35x+7y+1113-21x=\text{ 1659} \\ 14x\text{ + 7y = 1659 - 1113} \\ 14x\text{ +7y = 546}\ldots\ldots\ldots.\ldots(6) \end{gathered}`
`\begin{gathered} 56x+21y\text{ +}371-7x=2240 \\ 49x+21y=\text{ 2240 -371} \\ 49x\text{ +21y =1869 }\ldots.\ldots..\ldots\ldots\ldots...(7) \end{gathered}`

Subtracting equation 7 and 6 we have

3 x: 14x +7y = 546

1x : 49x +21y=1869

------------------------------

42x +21y =1638

49x +21y = 1869

----------------------------

-7x + 0 = -231

x = -231/-7 = $33= Price of one hat

Substituting this value of x into equation (7), we have

49(33) +21y = 1869

21y = 1869 -1617

21y = 252

y = $12= price of one gold rabbit

Step 5

Find the value of z using equation 1

From 1

5(33) + 12 + 3z = 237

177 +3z= 237

3z = 237 -177

3z= 60

z= 60/3

z= $20

Step 6

Find the value of

4x + 7y + 2z

4(33) + 7(12) +2(20) =132 +84 + 40 = $256