Question

a local nursery carries 2 shrubs for every 7 pots of flowers. which combination of shrubs and flowers could the nursery carry?
a. 6 shrubs and 42 pots of flowers
b. 10 shrubs and 35 pots of flowers
c. 6 pots of flowers and 21 shrubs
a textbook company sells teacher editions and student editions in package deals. each package includes 3 teacher editions for every 65 student editions. which combination could a school order?
a. 9 teacher to 260 student editions
b. 12 teacher to 325 student editions
c. 12 teach

Explanation:

First Question (Nursery Shrubs and Flowers)

Step1: Find the ratio

The ratio of shrubs to flowers is \( \frac{2}{7} \). We need to check which option has the same ratio.

Step2: Check Option A

For A: \( \frac{6}{42}=\frac{1}{7}
eq\frac{2}{7} \) (Wait, no, \( \frac{6}{42}=\frac{1}{7} \)? Wait, 6/42 simplifies to 1/7? No, 6 divided by 42 is 1/7? Wait, no, 2/7: if we multiply numerator and denominator by 3, we get 6/21. Wait, no, the first option is 6 shrubs and 42 flowers. Wait, 2 shrubs for 7 flowers. So the ratio of shrubs to flowers is 2:7. Let's check each option's ratio of shrubs to flowers.

Option A: 6 shrubs, 42 flowers. Ratio \( \frac{6}{42}=\frac{1}{7} \). Not equal to \( \frac{2}{7} \). Wait, maybe I mixed up. Wait, the ratio is shrubs:flowers = 2:7. So for each option, calculate shrubs/flowers and see if it equals 2/7.

Option B: 10 shrubs, 35 flowers. \( \frac{10}{35}=\frac{2}{7} \) (because 10÷5=2, 35÷5=7). So that's correct. Wait, wait, earlier mistake. Let's recalculate:

Option A: 6/42 = 1/7. Not 2/7.

Option B: 10/35 = 2/7 (divide numerator and denominator by 5: 10÷5=2, 35÷5=7). So that's correct.

Option C: 21 shrubs, 6 flowers. \( \frac{21}{6}=\frac{7}{2} \), which is the reciprocal. So wrong.

Wait, maybe I misread the first option. Wait, the first option is A: 6 shrubs and 42 pots of flowers. So shrubs:flowers = 6:42 = 1:7. B:10:35=2:7. C:21:6=7:2. So the correct one is B? Wait, but let's check again.

Wait, the problem says "2 shrubs for every 7 pots of flowers". So shrubs/flowers = 2/7.

Option A: 6/42 = 1/7. No.

Option B: 10/35 = 2/7. Yes.

Option C: 21/6 = 7/2. No. So the answer is B.

Step1: Find the ratio

The ratio of teacher editions to student editions is \( \frac{3}{65} \). We need to check which option has the same ratio.

Step2: Check Option A

For A: \( \frac{9}{260} \). Let's see if 3/65 = 9/260. Cross - multiply: 3×260 = 780, 9×65 = 585. Not equal.

Step3: Check Option B

For B: \( \frac{12}{325} \). Cross - multiply: 3×325 = 975, 12×65 = 780. Wait, no. Wait, 3/65: if we multiply numerator and denominator by 4, we get 12/260. Wait, the option B is 12 teacher to 325 student. Wait, maybe the third option is cut off, but among A and B, let's recalculate.

Wait, the ratio is 3 teacher : 65 student. So teacher/student = 3/65.

Option A: 9 teacher, 260 student. 9/260. Let's simplify 3/65: multiply numerator and denominator by 3: 9/195. 9/260 is not equal to 9/195.

Option B: 12 teacher, 325 student. 12/325. Simplify 3/65: multiply numerator and denominator by 4: 12/260. 12/325 is not equal to 12/260. Wait, maybe there's a typo, but assuming the options given, let's check again. Wait, 3/65 = 12/260 (multiply numerator and denominator by 4). If option B is 12 teacher to 325 student, that's not. But maybe the third option is 12 teacher to 260 student? But the given options: A is 9 to 260, B is 12 to 325. Wait, maybe I made a mistake. Wait, 3/65: let's check 12/325. 3×4 = 12, 65×5 = 325. No, 65×4 = 260. So 3×4=12, 65×4=260. So 12 teacher to 260 student. But if option B is 12 to 325, that's not. Wait, maybe the first question's answer is B, and for the second question, assuming the correct option is B (maybe the original problem has a typo, but based on the given, let's proceed).

Wait, for the first question, the correct option is B (10 shrubs and 35 pots of flowers) because 10/35 = 2/7.

For the second question, the ratio is 3 teacher : 65 student. Let's check option B: 12 teacher, 325 student. 3/65 = 12/325? Cross - multiply: 3×325 = 975, 12×65 = 780. Not equal. Option A: 9 teacher, 260 student. 3×260 = 780, 9×65 = 585. Not equal. Wait, maybe the third option is 12 teacher to 260 student, which would be correct (3×4=12, 65×4=260). But since the options given are A:9 to 260, B:12 to 325, maybe there's a mistake. But based on the first question, the answer is B.

Answer:

B. 10 shrubs and 35 pots of flowers

Second Question (Textbook Company)