Question

6th grade math review - unit 3 name: 1 at sweet delights bakery, there are 5 trays of croissants and 16 trays of muffins. what does the ratio 5:16 represent in this scenario? explain _____________________ ___________________ _____________________ 2 a school library has 240 books. the ratio of fiction books to non - fiction books is 3:5. if a student checks out 10 fiction books, what is the new ratio of fiction books to non - fiction books? circle all that are true. a 2:5 b 6:10 c 8:15 d 16:30 e 20:30 f 43:75 3 samir makes 180 grams of trail mix by combining 2 parts almonds with 3 parts cashews. how many grams of cashews does he use in all? show your work!

Explanation:

Question 1

Step1: Identify the quantities

The bakery has 5 trays of croissants and 16 trays of muffins.

Step2: Interpret the ratio

A ratio \( a:b \) compares the quantity of \( a \) to \( b \). Here, \( 5:16 \) compares the number of croissant trays to muffin trays.

Step1: Find total parts

The ratio of fiction to non - fiction is \( 3:5 \), so total parts \( = 3 + 5=8 \).

Step2: Find number of fiction and non - fiction books

Total books = 240. Number of fiction books \(=\frac{3}{8}\times240 = 90\). Number of non - fiction books \(=\frac{5}{8}\times240 = 150\).

Step3: Update fiction books

After checking out 10 fiction books, new number of fiction books \(=90 - 10 = 80\).

Step4: Find new ratio

New ratio of fiction to non - fiction is \( 80:150 \). Simplify this ratio by dividing both by 10: \( 8:15 \). Also, \( 80:150=\frac{80\times0.2}{150\times0.2}=16:30 \) (multiplying numerator and denominator by 0.2) and \( 80:150=\frac{80\times0.25}{150\times0.25}=20:37.5\) (wait, no, earlier calculation: \( 80:150=\frac{80\div10}{150\div10}=8:15\); \( 8:15=\frac{8\times2}{15\times2}=16:30\); \( 8:15=\frac{8\times\frac{5}{3}}{15\times\frac{5}{3}}=\frac{40}{3}:25\) (no, better to check options). Option C is \( 8:15 \), Option D is \( 16:30 \) (since \( 8:15 = 16:30 \) by multiplying numerator and denominator by 2), Option A: \( 2:5=\frac{2}{5}=0.4 \), \( 8:15\approx0.533 \), not equal. Option B: \( 6:10 = 0.6\), not equal. Option E: \( 20:30=\frac{2}{3}\approx0.666 \), not equal. Option F: \( 43:75\approx0.573 \), not equal. So the correct options are C and D.

Step1: Find total parts

The ratio of almonds to cashews is \( 2:3 \), so total parts \(=2 + 3 = 5\) parts.

Step2: Find weight per part

The total weight of trail mix is 180 grams. So weight per part \(=\frac{180}{5}=36\) grams.

Step3: Find weight of cashews

Cashews are 3 parts, so weight of cashews \(=3\times36 = 108\) grams.

Answer:

The ratio \( 5:16 \) represents the ratio of the number of trays of croissants to the number of trays of muffins.

Question 2