Question

Student council is selling Roses and Candy Grams for Valentine's Day. Each Candy Gram costs $1.50

and each Rose costs $2.00. The student council made $368 from their sales. They sold a total of 217
Roses and Candy Grams. How many roses were sold? Show all your work for full marks! (Solve the linear
system using substitution or elimination).
Letr represent
Let c represent
I

Answer 1

To solve this problem, we can set up a system of equations and use the elimination method to find the number of roses sold. The number of roses sold is 85.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's use the variables r and c to represent the number of roses and candy grams sold, respectively.

We know that each rose costs $2.00 and each candy gram costs $1.50. The student council made a total of $368 from their sales.

So, we can set up the following equations:

2r + 1.5c = 368 (equation 1)

r + c = 217 (equation 2)

To solve this system of equations, we can use the substitution or elimination method.

Let's solve it using the elimination method.

Multiply equation 2 by 1.5 to make the coefficients of c in both equations equal:

1.5(r + c) = 1.5(217)

1.5r + 1.5c = 325.5 (equation 3)

Now, subtract equation 3 from equation 1:

(2r + 1.5c) - (1.5r + 1.5c) = 368 - 325.5

0.5r = 42.5

Divide both sides of the equation by 0.5 to solve for r:

r = 42.5 / 0.5

r = 85

Therefore, 85 roses were sold.

Answer 2

Number of Roses sold = 132

Number of Candy Grams sold = 85

Step-by-step explanation:

Let the number of Roses sold =
`r`

Let the number of Candy Grams sold =
`c`

Cost of one Rose = $1.50

Cost of
`x` Roses = $1.50
`r`

Cost of one Candy Gram = $2.00

Cost of
`y` Candy Grams =
`\$2.00 * c`

Total number of Roses and Candy Grams sold = 217

i.e.

`r+c=217 ..... (1)`

Total cost = $368

Writing equation as per question statement:

`\$1.50r+\$2.00c=\$368 ..... (2)`

Using elimination method, let us eliminate
`y` of the two equations.

Multiplying equation (1) with 2 and subtracting equation (2) from it:

`0.50r=2* 217 - 368\\\Rightarrow 0.50r=434 - 368\\\Rightarrow 0.50r=66\\\Rightarrow r=132`

By equation (1):

`c=217-132\\c=85`

So, the answer is:

Number of Roses sold = 132

Number of Candy Grams sold = 85