Question

Taylor purchased three types of items (bags of candy, picture frames, and some packs of stickers) from a store. The bags of candy are $1, the picture frames are $2, and the packs of stickers are $3. Taylor spent a total of $16 on 9 items, and purchased three times as many bags of candy as she did packs of stickers. How many of each item did she purchase?

If x = the number of bags of candy, y = the number of picture frames, and z = the number of packs of stickers, which equation is not needed to model this situation?
A) x = 3z
B) z = 3x
C) z = x3
D) x + y + z = 9

Answer 1

1) 3 bags of candy, 5 picture frames and 1 pack of stickers

2) Both option B and C should be eliminated

Explanation:

Now according to the data given, total number of items bought is

x + y + z = 9 . . . (A)

Since, total cost is $16, and we know the unit cost of each item

so for x, total cost is number of items multiply by unit price

Total cost for x = (1) x (x)

for y, total cost is number of items multiply by unit price

Total cost for y = (2) x (y)

for z, total cost is number of items multiply by unit price

Total cost for z = (3) x (x)

So equation for total cost is

x + 2y + 3z = 16 . . .(B)

As we know by the data given that bags of candy are three times as compared to stickers

So, x = 3z

putting value of x in equation (A)

3z + y + z = 9

4z + y = 9 or y = 9 - 4z

Putting value of x and y in terms of z in equation B, we get

3z + 2(9 - 4z) + 3z = 16

6z + 18 - 8z = 16

-2z = -2

z = 1

Now x = 3z, so x = 3

and also y = 9 - 4z, so y = 5

so Taylor purchased

3 bags of candy, 5 picture frames and 1 pack of stickers

Now for the equations given below

A is valid because question tells that Taylor bough 3 bags of candy as compared to one pack of stickers and since total number of items purchased is equal to 9, so D is also right.

It might be possible that in options B and C it is typo error, but both donot fulfill the situation given in the question.

Answer 2

D

Explanation:

To write an expression and equation, define the variables.

Taylor purchased three types of items:

x = number of bags of candy

y = number of picture frames

z = number of stickers.

We know she bought 9 items.

So x+y+z = 9.