June 2023 Algebra 1 Regents Part IV

This exam was adminstered in June 2023. These answers were not posted until after the Independence Holiday weekend, well after the school year ednded.

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June 2023

Part IV: Each correct answer will receive 6 credits. Partial credit can be earned.


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.

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.

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

d = -2r + 18.92 and then substitute it into the first equation. 3r + 2(-2r + 18.92) = 31.88 and solve for r.

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.

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