Question

A single gram of a certain metallic substance has 0.52 grams of copper and 0.26 grams of zinc. The remaining portion of the substances is nickel. Ben estimated that 0.2 gram of nickel is 1 gram of the substance. He used this to estimate the amount of nickel in 35 grams of the substance. Find the result of Ben’s estimation strategy. Then, find the exact amount of nickel in 35 grams of the substance.

Answer 1

Ben's estimation strategy resulted in an estimation of 7 grams of nickel in 35 grams of the substance. However, the exact amount of nickel in 35 grams of the substance is 7.7 grams.

Step-by-step explanation:

To find the result of Ben's estimation strategy, we can use the given ratio that states 0.2 gram of nickel is equal to 1 gram of the substance.

So, if 1 gram of the substance has 0.2 grams of nickel, then 35 grams of the substance will have 35 * 0.2 = 7 grams of nickel, according to Ben's estimation.

However, we can find the exact amount of nickel in 35 grams of the substance using the given information. Let's first calculate the total amount of copper and zinc in 1 gram of the substance.

The total amount is 0.52 + 0.26 = 0.78 grams. Therefore, the amount of nickel in 1 gram of the substance is 1 - 0.78 = 0.22 grams.

To find the exact amount of nickel in 35 grams of the substance, we can set up a proportion:

1 gram of substance / 0.22 grams of nickel = 35 grams of substance / x grams of nickel

Cross-multiplying, we get:

x = (35 * 0.22) / 1 = 7.7 grams of nickel.

So, the exact amount of nickel in 35 grams of the substance is 7.7 grams, which is different from Ben's estimation of 7 grams.

Answer 2

Ben's estimation strategy gives him an answer of 7 g of nickel in 35 g of the substance.
The exact answer is there is 7.7 g of nickel in 35 g of the substance.

Using a proportion for Ben's estimate, we set the first ratio as 0.2/1, since he states there are around 0.2 g of nickel in 1 g of the substance. The other ratio would be x/35, with x representing the amount of nickel and 35 being the amount of the substance:

0.2/1 = x/35

Cross multiply:
0.2*35 = 1*x
7 = x

Ben's estimate is 7.

There are 0.52 g of copper and 0.26 g of zinc in 1 g of the substance. This makes up 0.52+0.26 = 0.78 g out of 1 g total. To find the remaining amount (nickel), subtract from 1:
1 - 0.78 = 0.22

There are 0.22 g of nickel in 1 g of the substance.

This means there are 0.22*35 = 7.7 g of nickel in 35 g of the substance.