Question

Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114, or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost ?

Answer 1

Answer:

The cost of each shirt is 16$ and the cost of each sweater is 33$

Solution:

Let us consider “x” as the cost of each shirt and “y” as the cost of each sweater.

From question, Andrea has bought 3 shirts and 2 sweaters for 114$. Hence we form equation as,

3x + 2y = 114 ------  eqn 1

Similarly, Andrea has bought 2 shirts and 4 sweaters for $164. Hence we form equation as,

2x + 4y = 164 ----- eqn 2

By solving equation 1 and equation 2, we get the value of “x” and “y”.

On multiplying equation 1 by 2,we get  

6x + 4y = 228 -------- eqn 3

Now solving eqn 2 and eqn 3

6x + 4y = 228                      

-2x - 4y = -164      

4x + 0y = 64

4x = 64

$x = \frac{64}{4}$

x = 16

Substituting the value of x in eqn 1, we get

3(16) + 2y = 114

48 + 2y = 114

2y = 114 - 48

2y = 66

$y = \frac{66}{2}$

y = 33

Thus the values of x and y are 16 and 33. So the cost of each shirt is 16$ and the cost of each sweater is 33$

Answer 2

Answer:

The cost of a shirt is $16 and the cost of a sweater is $33

Step-by-step explanation:

Let

x -----> the cost of a shirt

y -----> the cost of a sweater

we know that

$3x+2y=114$ -----> equation A

$2x+4y=164$----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

The solution is the point (16,33)

see the attached figure

therefore

The cost of a shirt is $16 and the cost of a sweater is $33