Harry had $32. He spent all the money buying three notebooks for x dollars each and four packs of index cards for y dollars each. If Harry had bought five notebooks and five packs of index cards, he would have run short by $18. The following system of equations models this scenario:

3x + 4y = 32
5x + 5y = 50

Use the system of equations to solve for x and y.

(8, 2)
(1, 5)
(2, 8)
(5, 1)

Question

Harry had $32. He spent all the money buying three notebooks for x dollars each and four packs of index cards for y dollars each. If Harry had bought five notebooks and five packs of index cards, he would have run short by $18. The following system of equations models this scenario:

3x + 4y = 32
5x + 5y = 50

Use the system of equations to solve for x and y.

(8, 2)
 (1, 5)
 (2, 8)
 (5, 1)

CheeseStick7793 · Answer

3x+4y=32 ( here is spent all money so I add 32 here )

5x+5y=50

by elemination method

3x+4y=32×5

5x+5y=50×4 ( here I'm going to eliminate y )

15 x+20y= 160

20x+20y= 200

- - = -

____________

-5x = -40

x = - 40 / -5

x = 8

here - × - = + so iam taking positive 8

now substitute the value of x in any equation

3×8+4y = 32

24 + 4y = 32

4y = 32-24

y = 8 / 4

y = 2

CHECKING

SUBSTITUTE BOTH VALUES IN ANY EQUATION

5×8+5×2 = 50

40 + 10 = 50

50 = 50

CheeseStick7793 · Answer

x = 8
y = 2