Question

Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month. To model the situation, she creates this equation, where x represents the number of months and y represents the total amount in her emergency fund: y = 2,000 + 320x Determine the missing steps and justifications in her work. y-2,000 = 2,000 + 320x - 2,000 10,000 -2,000 320 = 25 = x 8,000-200 320 y-2,000 2,000-320x2,000 division property of equality y-320 2,000 multiplication property of equality = 24 = x Steps y = 2,000 + 320x y-2,000 = 320x y-2,000 320x 320 320 y-2,000 320 given Justification subtraction property of equality simplification simplification substitution and simplification =X​

Answer 1

To determine the missing steps and justifications in Stella's work, let's go through the given equation and the steps she took:

1. Stella creates the equation: y = 2,000 + 320x, where y represents the total amount in her emergency fund and x represents the number of months.

2. Stella subtracts 2,000 from both sides of the equation: y - 2,000 = 2,000 + 320x - 2,000. This step is correct and follows the subtraction property of equality.

3. On the right side of the equation, Stella simplifies: 2,000 + 320x - 2,000. The 2,000 terms cancel out, leaving 320x. This step is correct.

4. Stella writes: 10,000 - 2,000 = 320x. This step is incorrect. The equation should still be y - 2,000 = 320x.

5. Stella divides both sides of the equation by 320: (y - 2,000)/320 = (320x)/320. This step is correct and follows the division property of equality.

6. On the right side of the equation, Stella simplifies: (320x)/320. The 320 terms cancel out, leaving x. This step is correct.

7. Stella writes: 8,000 - 200 = x. This step is incorrect. The equation should still be (y - 2,000)/320 = x.

8. Stella multiplies both sides of the equation by 320: 320 * (y - 2,000)/320 = x * 320. This step is correct and follows the multiplication property of equality.

9. On the left side of the equation, Stella simplifies: 320 * (y - 2,000)/320. The 320 terms cancel out, leaving y - 2,000. This step is correct.

10. Stella writes: y - 2,000 = 320x. This step is correct.

Therefore, the missing steps and justifications in Stella's work are as follows:

4. The equation should still be y - 2,000 = 320x.

7. The equation should still be (y - 2,000)/320 = x.

By correcting these steps, Stella's work will be accurate.

Answer 2

To determine the missing steps and justifications in the student's work, subtract 2,000 from both sides of the equation and simplify to isolate y, then divide both sides of the equation by 320 to solve for x.

Step-by-step explanation:

The student's equation for Stella's emergency fund is correct: y = 2,000 + 320x. However, the missing steps and justifications in her work need to be filled in:

1. To isolate y, subtract 2,000 from both sides of the equation: y-2,000 = 2,000 + 320x - 2,000
2. Simplify the equation: y-2,000 = 320x
3. Divide both sides of the equation by 320 to solve for x: (y-2,000) / 320 = x