Answer: Choice B) 60 roses and 10 carnations
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Explanation:
- r = number of roses
- c = number of carnations
r and c are positive whole numbers.
r+c = total number of flowers = 50, since 50 orders are made.
The first equation to set up is r+c = 50.
This equation can be solved to get r = 50-c.
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3r = cost of all the roses only, in dollars
1.5c = cost of all the carnations only, in dollars
3r+1.5c = total cost of all the flowers = 195 dollars
3r+1.5c = 195
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Let's apply substitution to solve
3r+1.5c = 195
3(50-c)+1.5c = 195
150-3c+1.5c = 195
-1.5c+150 = 195
-1.5c = 195-150
-1.5c = 45
c = 45/(-1.5)
c = -30
That's not good. We shouldn't get a negative value.
It turns out that the condition r+c = 50 should be ignored. Notice how none of the answer choices listed have r+c leading to 50.
So we'll only focus on the equation 3r+1.5c = 195
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If we plugged in r = 100 and c = 100, then we get
3r+1.5c = 195
3(100)+1.5(100) = 195
300+150 = 195
450 = 195
Which is false. So we can rule out choice A
Let's repeat those steps for choice B
3r+1.5c = 195
3(60)+1.5(10) = 195
180 + 15 = 195
195 = 195
So that works out. I have a feeling your teacher meant to say "70 orders" instead of "50 orders". If so, then the equation r+c = 50 would be r+c = 70 and everything would lead to choice B as the final answer.
Choices C and D are similar to that of choice A, so they can be ruled out.
