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## A chili recipe calls for the final mixture to consist of 1/2

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### A chili recipe calls for the final mixture to consist of 1/2

by vinni.k » Mon Nov 26, 2018 8:14 am

00:00

A

B

C

D

E

## Global Stats

A chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices. If a total of 6 pounds of sauce and spices are used, how many pounds of beans are used?

A. 3
B. 6
C. 12
D. 18
E. 24

OA is C

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by [email protected] » Mon Nov 26, 2018 9:25 am
vinni.k wrote:A chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices. If a total of 6 pounds of sauce and spices are used, how many pounds of beans are used?

A. 3
B. 6
C. 12
D. 18
E. 24
A chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices
Let's see what fraction of the final mixture is sauce and various spices
1/2 + 1/3 = 3/6 + 2/6 = 5/6
If 5/6 of the mixture is meat and beans, then the remaining 1/6 of the mixture is sauce and various spices

So, the mixture is 1/2 meat, 1/3 beans and 1/6 sauce and various spices

If a total of 6 pounds of sauce and spices are used, how many pounds of beans are used?
Notice that 1/3 is TWICE 1/6
This means the weight of beans in the mixture is TWICE the weight of sauce and spices in the mixture
So, if the mixture contains 6 pounds of sauce and spices, then it must contain 12 pounds of beans in the mixture

Cheers,
Brent
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by vinni.k » Mon Nov 26, 2018 4:17 pm
Thank you <i class="em em-pray"></i>
[email protected] wrote:
vinni.k wrote:A chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices. If a total of 6 pounds of sauce and spices are used, how many pounds of beans are used?

A. 3
B. 6
C. 12
D. 18
E. 24
A chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices
Let's see what fraction of the final mixture is sauce and various spices
1/2 + 1/3 = 3/6 + 2/6 = 5/6
If 5/6 of the mixture is meat and beans, then the remaining 1/6 of the mixture is sauce and various spices

So, the mixture is 1/2 meat, 1/3 beans and 1/6 sauce and various spices

If a total of 6 pounds of sauce and spices are used, how many pounds of beans are used?
Notice that 1/3 is TWICE 1/6
This means the weight of beans in the mixture is TWICE the weight of sauce and spices in the mixture
So, if the mixture contains 6 pounds of sauce and spices, then it must contain 12 pounds of beans in the mixture

Cheers,
Brent

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by [email protected] » Mon Nov 26, 2018 7:06 pm
Hi vinni.k,

We're told that a chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices (and a total of 6 pounds of sauce and spices are used). We're asked how many pounds of beans are used. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. Let's TEST Answer B first.

IF... there are 6 pounds of beans, then the total mixture is 3(6) = 18 pounds TOTAL
(1/2)(18 pounds) = 9 pounds of meat
However, 9 pounds of meat + 6 pounds of beans + 6 pounds of sauce/spices = 21 pounds. This does NOT match the total we calculated. We need the total to be larger, so we need more beans. 18 pounds and 21 pounds are relatively close to one another; Answer B doubles the beans, while Answer C triples the beans. Let's TEST the smaller increase first...

IF... there are 12 pounds of beans, then the total mixture is 3(12) = 36 pounds TOTAL
(1/2)(36 pounds) = 18 pounds of meat
However, 18 pounds of meat + 12 pounds of beans + 6 pounds of sauce/spices = 36 pounds. This matches the total we calculated, so this must be the answer.

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by vinni.k » Wed Nov 28, 2018 5:45 am
thanks <i class="em em-pray"></i>
[email protected] wrote:Hi vinni.k,

We're told that a chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices (and a total of 6 pounds of sauce and spices are used). We're asked how many pounds of beans are used. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. Let's TEST Answer B first.

IF... there are 6 pounds of beans, then the total mixture is 3(6) = 18 pounds TOTAL
(1/2)(18 pounds) = 9 pounds of meat
However, 9 pounds of meat + 6 pounds of beans + 6 pounds of sauce/spices = 21 pounds. This does NOT match the total we calculated. We need the total to be larger, so we need more beans. 18 pounds and 21 pounds are relatively close to one another; Answer B doubles the beans, while Answer C triples the beans. Let's TEST the smaller increase first...