On a Recent Trip to the Market Word Problem

Question

On a recent trip to the market, you purchased 2 gallons of milk, 5 bottles of water, and 6 bags of chips. Your total bill (before tax) was $19.00. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $2.00 more than a bottle of water, how much does each item cost?

(a) Define your variables.

(b) Set up a linear system in three variables.

(c) Use your linear system to set up an augmented matrix.

(d) Using RREF, determine how much each item costs.

Answer 1

M+W+C = 1900

W=2C

M=W+200=2C+200

2C+200 + 2C + C = 1900

5C = 1700

C = 1700/5

C= $3.40 for a bag of Chips

W=2C = $6.80 for 5 bottles of Water

M=W+200 = $8.80 for 2 gallons of Milk

340+680+880= 1900

if you set up a matrix you and solve for M,W and C you should get the same answer

1st column are M values, 2nd: W, 3rd C

| 1 1 1 | 1900|

| 0 -1 2 | 0|

| 1 -1 0 | 200|

use row operations to get

| 1 0 0 | 880 |

| 0 1 0 | 680 |

| 0 0 1 | 340 |