The Miller family

Question

The Miller family has two hundred forty acres of farmland that is in the shape of a rectangle. The Miller family plants crops on all the farmland. The Miller family plants corn on one-half of the farm land. The Miller family plants oats on one-fourth of the farmland. The Miller family plants the rest of the farmland in equal amounts of cucumbers and beans. How many acres of farmland are used to plant each type of crop? Show all your mathematical thinking.

Answer 1

[Observe: We do NOT have to calculate each crop individually, starting from 240 acres! This speeds up the solution. Using shortcuts is a critical skill on a test day. That's what I teach]

[Whatever is in the brackets below can be done mentally]

Corn = 1/2 _* 240 = 120 acres

Oats = 1/2 Corn [1/4 = (1/2) / 2] = 1/2 _* 120 = 60 acres

Beans = 1/2 of the rest [240 - 120 - 60 = 60 ] = 1/2 _* 60 = 30 acres

Cucumbers = Beans = 30 acres

Answer:

Corn 120 acres

Oats 60 acres

Beans 30 acres

Cucumbers 30 acres

Answer 2

corn = 1/2 x 240 = 240/2 = 120 acres

oats = 1/4 x 240 = 240/4 = 60 acres

beans = 1/8 x 240 = 240/8 = 30 acres

cucumbers= 1/8 x 240 = 240/8 = 30 acres

Answer 3

Hello, thank you for taking the time to post your question!

First you can just find the Corn and Oats acreage directly by multiplying by the proportion that has been planted in those. That means:

Corn: 240 x ½ = 120 acres

Oats: 240 x ¼ = 60 acres

What’s remaining then is 240 – 120 – 60 = 60 acres

Half is Beans and Half is Cucumbers so that would be

Beans: 60 acres x ½ = 30 acres

Cucumbers: 60 acres x ½ = 30 acres

I hope that helps get you moving in the right direction! Feel free to reach out if you still have questions beyond that :)

Answer 4

For the corn, the Miller family needs to use 1/2 of their 240 acres. (1/2)(240)=120 acres

For the oats, their need 1/4, so (1/4)(240)=60 acres

That leaves 60 acres to be equally split between cucumbers and beans, so 1/2(60) gives us 30 acres of cucumber and 30 acres of beans. (Alternatively, you could think of the remaining land 1/4 of of the original, and splitting that equally would be 1/8 for each).

Answer 5

corn = (1/2)(240)

oats = (1/4)(240)

beans = (1/8)(240)

cucumbers = (1/8)(240)