Math  /  Algebra

Question3 3.1
Gaston bought two types of candies: red candies that cost $0.60\$ 0.60 each and green candies that each cost zz times as much as a red candy. If the cost of 3 red candies and 1 green candy was $3\$ 3, what is the value of zz ?

Studdy Solution

STEP 1

What is this asking? We need to figure out how many times more expensive a green candy is than a red candy, given the total cost of a mixed bag. Watch out! Don't mix up the cost of the red candies with the cost of the green candies!

STEP 2

1. Calculate the cost of the red candies.
2. Calculate the cost of the green candy.
3. Determine the value of *z*.

STEP 3

We know that Gaston bought **3** red candies, and each red candy costs $0.60\$0.60.
So, let's multiply the number of red candies by the cost of each red candy to find the **total cost** of the red candies.

STEP 4

Total cost of red candies=3$0.60=$1.80\text{Total cost of red candies} = 3 \cdot \$0.60 = \$1.80 So, the red candies cost a total of $1.80\$1.80.

STEP 5

We know that Gaston spent a total of $3.00\$3.00, and we just figured out that the red candies cost $1.80\$1.80.
The rest of the money must have been spent on the green candy!
Let's subtract the cost of the red candies from the total cost to find the cost of the **single** green candy.

STEP 6

Cost of green candy=$3.00$1.80=$1.20\text{Cost of green candy} = \$3.00 - \$1.80 = \$1.20 Great! The green candy cost $1.20\$1.20.

STEP 7

Remember, the problem tells us that a green candy costs *z* times as much as a red candy.
We know the cost of one green candy ($1.20\$1.20) and the cost of one red candy ($0.60\$0.60).
We can set up an equation to solve for *z*.

STEP 8

Cost of green candy=zCost of red candy\text{Cost of green candy} = z \cdot \text{Cost of red candy} Let's plug in the values we know: $1.20=z$0.60\$1.20 = z \cdot \$0.60

STEP 9

To solve for *z*, we need to divide to one.
We can do this by dividing both sides of the equation by $0.60\$0.60: $1.20$0.60=z$0.60$0.60\frac{\$1.20}{\$0.60} = \frac{z \cdot \$0.60}{\$0.60} 2=z2 = z

STEP 10

Therefore, the value of *z* is **2**.
This means a green candy is twice as expensive as a red candy!

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