Sasha reads at a rate of 0.8 pages per minute in her favorite novel, but only 0.5 pages per minute in the autobiography she is currently reading. Her English class has a minimum reading requirement of at least 75 pages per week. This situation is represented by the inequality 0.8n+0.5a≥75, where n is the number of minutes she reads her novel and a is the number of minutes she reads the autobiography.
Which statement correctly explains a solution for this situation?
If Sasha reads the autobiography for 32 minutes, she can meet the minimum reading requirement by reading her novel for 62 minutes.
If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
If Sasha reads the autobiography for 94 minutes, she meets the minimum reading requirement without reading any of her novel.
If Sasha reads her novel for 32 minutes, she can meet the minimum reading requirement by reading the autobiography for 62 minutes.
If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
To determine the correct solution for the given situation, we need to find a combination of minutes spent reading Sasha's novel (n) and minutes spent reading the autobiography (a) that satisfies the inequality 0.8n + 0.5a ≥ 75.
Let's consider each statement and check if it satisfies the inequality:
1. If Sasha reads the autobiography for 32 minutes, she can meet the minimum reading requirement by reading her novel for 62 minutes.
Substituting the values into the inequality: 0.8 * 62 + 0.5 * 32 = 49.6 + 16 = 65.6
The result, 65.6, is not greater than or equal to 75. Therefore, this statement is incorrect.
2. If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
Substituting the values into the inequality: 0.8 * 94 + 0.5 * 0 = 75.2 + 0 = 75.2
The result, 75.2, is greater than or equal to 75. Therefore, this statement is correct.
3. If Sasha reads the autobiography for 94 minutes, she meets the minimum reading requirement without reading any of her novel.
Substituting the values into the inequality: 0.8 * 0 + 0.5 * 94 = 0 + 47 = 47
The result, 47, is not greater than or equal to 75. Therefore, this statement is incorrect.
4. If Sasha reads her novel for 32 minutes, she can meet the minimum reading requirement by reading the autobiography for 62 minutes.
Substituting the values into the inequality: 0.8 * 32 + 0.5 * 62 = 25.6 + 31 = 56.6
The result, 56.6, is not greater than or equal to 75. Therefore, this statement is incorrect.
Based on the analysis above, the correct solution for this situation is:
If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
To find the correct solution, we need to substitute the given values for n and a into the inequality 0.8n + 0.5a ≥ 75 and check if the inequality is satisfied.
For the first option: If Sasha reads the autobiography for 32 minutes and the novel for 62 minutes, we substitute n = 62 and a = 32 into the inequality: 0.8(62) + 0.5(32) ≥ 75. Calculating this, we get 49.6 + 16 ≥ 75, which simplifies to 65.6 ≥ 75. However, this inequality is not true, so the first option is not correct.
For the second option: If Sasha reads her novel for 94 minutes and does not read any of the autobiography, we substitute n = 94 and a = 0 into the inequality: 0.8(94) + 0.5(0) ≥ 75. Calculating this, we get 75.2 + 0 ≥ 75, which simplifies to 75.2 ≥ 75. Since this inequality is true, the second option is the correct solution.
For the third option: If Sasha reads the autobiography for 94 minutes and does not read any of her novel, we substitute n = 0 and a = 94 into the inequality: 0.8(0) + 0.5(94) ≥ 75. Calculating this, we get 0 + 47 ≥ 75, which simplifies to 47 ≥ 75. However, this inequality is not true, so the third option is not correct.
For the fourth option: If Sasha reads her novel for 32 minutes and the autobiography for 62 minutes, we substitute n = 32 and a = 62 into the inequality: 0.8(32) + 0.5(62) ≥ 75. Calculating this, we get 25.6 + 31 ≥ 75, which simplifies to 56.6 ≥ 75. However, this inequality is not true, so the fourth option is not correct.
Therefore, the correct statement explaining a solution for this situation is: If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
.8 * 62 +.5 *32 = 49.6 +16 = 65.6 no
but
.8 * 94 = 75.2 which works
so forget the autobiography