Determine whether the following equations are correct or incorrect and briefly explain your reasoning. Asia and Taryn each had the same amount of money. After Asia spent $8 and Taryn spent $16, the...

Determine whether the following equations are correct or incorrect and briefly explain your reasoning.

1. 
   

   Asia and Taryn each had the same amount of money. After Asia spent $8 and Taryn spent $16, the ratio of Asia’s money to Taryn’s money was 4 to 3. How much money did each girl have at first? An equation appropriate for solving this problem is 3(X – 8) = 4(X – 16).

   
   


2. 
   

   A company mixes fertilizer and soil in a 4 to 9 ratio by weight, but the amounts of fertilizer and soil the company mixes vary. Let F be an unspecified number of kg of fertilizer, which can vary, and let S be the corresponding number of kg of soil the company might use. An equation representing this situation is 9S = 4F.

   
   


3. 
   

   If 10 workers take 8 hours to sew a store’s order of pants, then how long would 15 workers take to sew the store’s order of pants, assuming all workers work at the same steady rate and all the pants are the same? An equation appropriate for solving this problem is 8 hours / 10 workers = X hours / 15 workers.

   
   


4. 
   

   A company makes mixtures of acetic acid and water such that the acetic acid is 15% of the total mass (weight) of the mixture. Let A be an unspecified number of grams of acetic acid, which can vary, and let W be the corresponding number of grams of water in this type of mixture. An equation that relates A and W is A = (3/17) W.