Question

Solve the problem using dimensional analysis. Every number must have a unit. Work must be shown. Conversion factors are in the table.
Gold cost $8.00 per ounce. Determine how many grams you can purchase for $15.00.

Answer 1

Dimensional analysis is based on the principle that physical quantities that are equated must be represented in measures of the same basic quantities (e.g mass, length, or time) in order to draw conclusions about their relationships.

If Gold cost $8.00 per ounce

Then $15.00 will cost:

$\mathbf{x = \dfrac{\ 15.00 \times 1 \ ounce}{ \ 8.00}}$

x = 1.875 ounces

Assuming x to be the amount of ounce, then Gold of $15.00 will cost 1.875 ounces.

Now, given that:

1000g = 1kg

1 kg = 2.2 lbs

1 lb = 16 oz

Then, to determine the amount of gram that is equivalent to 1.875 ounces, we have:

Since 1 lb = 16 oz

2.2 lbs = (2.2*16) oz

= 35.2 oz

Since 1 kg = 2.2lbs = 35.02 oz

∴

x(g) =  1 kg

1000 g = 35.02 oz

1 (g) = 35.02/1000 oz

1 (g) = 0.03502 oz

Thus, If 1 (g) = 0.03502 oz

x(g) = 1.875 oz

$\mathbf{x(g) = \dfrac{1.875 \ oz \times 1 \ g}{0.03502 \ oz}}$

x  = 53.54 g

Thus, we can conclude that amount of the grams you can purchase for $15.00 is 53.54 grams

Learn more about dimensional analysis here:

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