Lesson 12
Solving More Ratio Problems
Let’s compare all our strategies for solving ratio problems.
Problem 1
Describe a situation that could be represented with this tape diagram.
![Tape diagram, blue parts, 3 and green parts, 2. Each part labeled 6.](https://cms-im.s3.amazonaws.com/aAoGChBTfwqRhFF7WQGYaY5V?response-content-disposition=inline%3B%20filename%3D%226-6.2.E2.PP.Image.Rev.0101.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.E2.PP.Image.Rev.0101.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232449Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b6209e2459323b734e01ca85ba8995a4bfc379e21ecbab0d26f28e0408aac8c9)
Problem 2
There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total.
- How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning.
- How much are the coins in the piggy bank worth?
Problem 3
Two horses start a race at the same time. Horse A gallops at a steady rate of 32 feet per second and Horse B gallops at a steady rate of 28 feet per second. After 5 seconds, how much farther will Horse A have traveled? Explain or show your reasoning.
Problem 4
Andre paid $13 for 3 books. Diego bought 12 books priced at the same rate. How much did Diego pay for the 12 books? Explain your reasoning.
Problem 5
Which polyhedron can be assembled from this net?
![A net composed of one equilateral triangle joined on each of its sides to a isosceles triangle.](https://cms-im.s3.amazonaws.com/P6xKRck2hn9qgUGjTHbxbsN8?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.18.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.18.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232449Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c6cf70bdddbc4616099a6a0726f637244e09772e66e5f4f75c834c2ab9097f1a)
A triangular pyramid
A trapezoidal prism
A rectangular pyramid
A triangular prism
Problem 6
Find the area of the triangle. Show your reasoning. If you get stuck, consider drawing a rectangle around the triangle.
![A slanted triangle drawn on a 7 by 7 grid.](https://cms-im.s3.amazonaws.com/tMLw3NK2ekEKRLp527tV3tq8?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP_Image_33.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP_Image_33.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232449Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=feab3aad94293a10e3f03e93088c8c4c43163b3092fa73c74bdcef1ad3b550a3)