Determinants and Cramer's Rule Confusion

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annabethannabeth

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Hello :)

I am in 11th-grade algebra. Today we are learning about determinants and Cramer's Rule. I understand the assignment pretty well, but they didn't show me how to apply it to word problems.

I am stuck on these 2 problems:
Corinne bought 5 bags of chips and 4 jars of dipping sauce for $21.82. At the same prices, Ginger bought 4 bags of chips and 3 jars of dipping sauce for $16.86. What is the price of one jar of dipping sauce?

Dee bought 6 dolls and 2 toy trains for $55. At the same prices, Joy bought 4 dolls and 7 toy trains for $65. What is the price of a doll?

If I could get some help even solving one so that I could solve the other that would be great. Thanks!
 
What if you never had heard of Determinants or Cramer's Rule. How would you solve one?
 
As mentioned above, solving this problem has nothing to do with your understanding of cramer's rule.
Get the system of equations and then use cramer's rule. Cramer's rule does NOT help you get the equations!
 
Let's make a start on the first:
annabethannabeth said:
Corinne bought 5 bags of chips and 4 jars of dipping sauce for $21.82. At the same prices, Ginger bought 4 bags of chips and 3 jars of dipping sauce for $16.86. What is the price of one jar of dipping sauce?
Click to expand...
What variables might you use? Maybe something like this (because you are asked for one of the prices):

x = price of one bag of chips​
y = price of one jar of dipping sauce​

Now try writing equations representing the two facts you are given:

Corinne bought 5 bags of chips and 4 jars of dipping sauce for $21.82.​
Ginger bought 4 bags of chips and 3 jars of dipping sauce for $16.86.​

Once you've done this, you'll have a system of equations, and you can apply Cramer's Rule.

Presumably you have seen word problems like this before, and solved them by other means. In fact, you might want to do that here, before or after using Cramer's Rule, just to see for yourself that it works -- even in word problems.
 
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