SOLVING WORD PROBLEMS USING INVERSE MATRIX

Problem 1 :

A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. How much is each bush and how much is each tree?

Solution:

Let x be the bushes and

y be the trees.

13x + 4y = 487

6x + 2y = 232

So, each bush is $23 and each tree is $47.

Problem 2 :

The admission fee at a small fair is $1.50 for children and $4 for adults. On a certain day, 220 people enter the fair and $5050 is collected. How many children attended the fair that day?

Solution:

Let x be the number of children and

y be the number of adults.

x + y = 220

1.50x + 4y = 5050

1668 children attended the fair that day.

Problem 3 :

Sam Stone bought 5 pieces of gum, 3 jawbreakers, and 2 candy bars for $1.04. Bill Bridge bought 2 pieces of gum, 12 jawbreakers, and 4 candy bars for $2.24. Mr. Bulldog bought 7 pieces of gum, 2 jawbreakers, and 1 candy bar for $0.74. Use matrix equations to determine the cost of each item.

Solution:

Let x be the gum, y be the jawbreakers and z be the candy bars.

5x + 3y + 2z = 1.04

2x + 12y + 4z = 2.24

7x + 2y + 1z = 0.74

So, each gum is $0.04, each jawbreaker is $0.08 and each candy bar is $0.3.

Problem 4 :

A gift shop has helium-filled balloons for all occasions priced according to size-small, medium, and large. B.D. Stone spent $17 for four small balloons, two medium balloons, and one large balloon. It cost Betty Bridge $22 for six small, one medium, and two large balloons. For $25, Henry Hay got four small, three medium, and two large balloons. How much did Clara Claiborne pay for three of each size?

Solution:

Let x be the small size balloons, y be the medium size  balloons and z be the large size balloons.

4x + 2y + z = 17

6x + y + 2z = 22

4x + 3y + 2z = 25