Solve the problem using dimensional analysis. Every number must have a unit. Work must be shown. Conversion factors are in the t

Question

3 years ago

14

able.
Gold cost $8.00 per ounce. Determine how many grams you can purchase for $15.00.

1 answer:

anygoal [31] · Answer 1 · 2022-12-18T22:58:21+03:00

The number of grams of gold you can purchase for $15 if Gold cost $8.00 per ounce is 53.26g

Dimensional analysis is a means of representing values using units.

From the question, we are told that Gold cost $8.00 per ounce, this means that:

$8.00 = 1 ounce

In order to calculate the amount in grams you can purchase for $15, we need to know the price in ounces first.

$15.00 = x

Divide both expressions

$\dfrac{8}{15} = \dfrac{1}{x}\\x = \dfrac{15}{8}\\x= 1.875 ounces$

Next is to convert the ounces to pounds.

1 pound = 16 ounces

y = 1.875 ounces

y = 1.875/16

y = 0.1171875 pounds

Conver 0.1171875 pounds to kg

Since 1kg = 2.2 pounds

z = 0.1171875 pounds

2.2z = 0.1171875

z = 0.1171875/2.2

z = 0.053267kg

Finally, convert 0.053267kg to grams using the conversion rate

1kg = 1000g

0.053267kg = y

y = 0.05326 * 1000

y = 53.26g

This shows that the amount of grams you can purchase for $15 is 53.26g