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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

Respuesta :

isyllus

Answer:

Number of Roses sold = 132

Number of Candy Grams sold = 85

Step-by-step explanation:

Let the number of Roses sold = [tex]r[/tex]

Let the number of Candy Grams sold = [tex]c[/tex]

Cost of one Rose = $1.50

Cost of [tex]x[/tex] Roses = $1.50 [tex]r[/tex]

Cost of one Candy Gram = $2.00

Cost of [tex]y[/tex] Candy Grams =  [tex]\$2.00 \times c[/tex]

Total number of Roses and Candy Grams sold = 217

i.e.

[tex]r+c=217 ..... (1)[/tex]

Total cost = $368

Writing equation as per question statement:

[tex]\$1.50r+\$2.00c=\$368 ..... (2)[/tex]

Using elimination method, let us eliminate [tex]y[/tex] of the two equations.

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

[tex]0.50r=2\times 217 - 368\\\Rightarrow 0.50r=434 - 368\\\Rightarrow 0.50r=66\\\Rightarrow r=132[/tex]

By equation (1):

[tex]c=217-132\\c=85[/tex]

So, the answer is:

Number of Roses sold = 132

Number of Candy Grams sold = 85

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