This exam was adminstered in June 2023. These answers were not posted until after the Independence Holiday weekend, well after the school year ednded.
More Regents problems.
June 2023
Part IV: Each correct answer will receive 6 credits. Partial credit can be earned.
If r represents the cost of one rose and d represents the cost of one daisy, write a system of
equations that models this situation.
Use your system of equations to algebraically determine both the cost of one rose and the cost of
one daisy.
If Dana had waited until the plants were on sale, she would have paid $4.50 for each rose and
$6.50 for each daisy. Determine the total amount of money she would have saved by buying all of
her flowers during the sale.
37. Dana went shopping for plants to put in her garden. She bought three roses and two daisies
for $31.88. Later that day, she went back and bought two roses and one daisy for $18.92.
Answer:
Write a system of equations. Remember to use r and d, not x and y. It will be solved the same way.
The second sentence tells us 3r + 2d cost 31.88. The third sentence says that 2r + 1d cost 18.92. So:
3r + 2d = 31.88
2r + d = 18.92
You can use either elimination or substition to solve this. To use substitution, rewrite the second equation as
Or use elimination, by multiplying the second equation by 2.
3r + 2d = 31.88
2r + d = 18.92
3r + 2d = 31.88
4r + 2d = 37.84
-r= -5.96
r = 5.96
1 rose costs $5.96.
2(5.96) + d = 18.92
11.92 + d = 18.92
d = 7
1 daisy costs $7.00.
The final portion of the question could be answered even if you didn't solve the system of equations. It could be solved even if you didn't WRITE the system of equations.
You already know how much money Dana spent. It's in the problem. Find how much she would have spent with the flowers on sale, and then subtract the two numbers.
(31.88 + 18.92) - (5*(4.50) + 3(6.50)) = $8.80
She would've saved $8.80.
As far as Part IV problems go, this one wasn't particularly difficult. It was basically a Part III question with an additional problem tacked onto the end of it.
End of Exam
How did you do?
More to come. Comments and questions welcome.
More Regents problems.
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