Question

lesson 14 | session 2
name:
practice solving ratio problems involving parts
and wholes
study the example showing how to solve ratio problems involving parts and
wholes. then solve problems 1–5.
example
jessie’s meatloaf recipe uses a ratio of 1 part pork to 3 parts beef. she wants
to make a meatloaf with 32 oz of meat. how many ounces of beef and how
many ounces of pork does jessie need for her meatloaf?
you can use a tape diagram to relate the parts to the total.
divide the total amount by
the number of equal parts
to find the value of each part.
32 oz ÷ 4 = 8 oz
pork: 1 × 8 oz = 8 oz
beef: 3 × 8 oz = 24 oz
jessie needs 8 oz of pork and 24 oz of beef.
1 in the example, suppose jessie wants to make a meatloaf with 40 oz of meat.
a. what changes would you need to make to the tape diagram?
b. how many ounces of pork and how many ounces of beef would jessie need?
2 a movie theater sells only adult tickets and child tickets.
for one movie, the theater sells 126 tickets in all. the tape
diagram shows the ratio of adult tickets to child tickets the
theater sells for the movie. what does each square of the
tape diagram represent?
a 9 tickets
b 14 tickets
c 18 tickets
d 28 tickets

Explanation:

Step1: Analyze the ratio from the tape diagram

From the tape diagram, adult tickets have 7 squares and child tickets have 2 squares. So the total number of parts (squares) is \(7 + 2=9\) parts? Wait, no, wait. Wait, the total tickets are 126. Wait, the ratio of adult to child tickets is the number of squares. Adult tickets: 7 squares, Child tickets: 2 squares. So total parts (squares) is \(7 + 2 = 9\)? Wait, no, wait, let's check again. Wait, the problem says "the tape diagram shows the ratio of adult tickets to child tickets the theater sells for the movie". So adult tickets are represented by 7 squares, child by 2 squares. So total number of squares (parts) is \(7+2 = 9\)? Wait, no, wait, 126 tickets in total. So each square represents \(126\div(7 + 2)\)? Wait, no, wait, 7 (adult) + 2 (child) = 9 parts? Wait, but 126 divided by 9 is 14? Wait, 914=126? Wait, 914=126? 1014=140, minus 114=14, so 126. Yes. Wait, but let's do it step by step.

Step2: Calculate total number of parts

The tape diagram for adult tickets has 7 squares and child tickets has 2 squares. So total number of parts (squares) is \(7+2 = 9\) parts? Wait, no, wait, 7 (adult) + 2 (child) = 9 parts. Wait, but 126 tickets in total. So each part (square) represents \(126\div(7 + 2)\)? Wait, no, 7 + 2 is 9? Wait, 7+2=9? Then 126 divided by 9 is 14? Wait, 9*14=126. So each square represents 14 tickets? Wait, but let's check the options. Option B is 14 tickets. Wait, but let's confirm.

Wait, adult tickets: 7 squares, child: 2 squares. Total squares: 7 + 2 = 9. Total tickets: 126. So each square (part) is \(126\div(7 + 2)=126\div9 = 14\). So each square represents 14 tickets. So the answer should be B.

Wait, but let's re - check. Total parts: 7 (adult) + 2 (child) = 9 parts. Total tickets: 126. So each part (square) is \(126\div9 = 14\). So each square represents 14 tickets, which is option B.

Answer:

B. 14 tickets