2. For a class picnic, two teachers went to the same store...

2. For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $22.30. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $17.90. Variables: Rates of change: Constants: Totals: Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w. Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara's prices are not possible. Solve your system of equations to determine the actual cost, in dollars, of each juice box and each bottle of water.

Transcript

00:01 Went to the same store to purchase drinks.

00:02 One teacher purchased 18 juice boxes in 32 bottles of water and spent $22 .30.

00:10 The other teacher purchased 14 juice boxes and 26 bottles of water and spent $17 .90.

00:17 So i'm going to use j for juice boxes and w for water.

00:30 The rates of change the constants and the totals.

00:36 So one teacher, so for the rate of change, i'm going to do 18 juice plus 32 bottles of water.

00:49 And then the other one is 14 juice for every 26 bottles of water.

00:58 And the constants would be the amount of money that was spent.

01:06 So that would be the 22 .30 and the 1790.

01:15 So write a system to represent the cost of the juice boxes in j and the water, the bottle of water, w.

01:25 So i'm going to have 18j plus 32w equals $22 and $30.

01:35 Then for the other one, it's 14j.

01:38 Plus 26 w equals $17 in 90 cents so then kara said that the juice boxes might have cost 52 cents each and the bottles of water might have cost 33 cents each use your system of equations to justify that kara's prices are not possible so i'm just going to set this up here 18 j plus 32 w equals $22 .30.

02:12 Then i have 14j plus 26w equals $22 .30.

02:21 I'm sorry, $17 .90.

02:29 So what i'm going to do now is i'm going to solve this via elimination.

02:35 And or before i do that, i'm going to input her 52 cents and or 32 cents and or 33 cents into the equation.

02:45 So, 52 cents each for the bottles of water, oh, juice boxes.

02:50 So 18 times 0 .52 plus 32 times 33 cents equals 2230.

03:02 So 18 times 0 .52 is $9 .36 plus 32 times $3 .3 is $30.

03:16 And 56 cents that does not equal $22 .30.

03:23 That's $10 .56 plus $9 .36.

03:27 That equals $19 .92.

03:33 It does not equal $22 .30...

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