Kim went shopping and made two purchases. the second purchase cost 9.50 less then the first purchase. Kim spent a total of 136.40. what was the amount of each p

Question

Write an equation to represent the given word problem.

Answer 1

What do we know?

Total purchases = 136.40

purchase 1 = x

purchase 2 = x - 9.50

Write the equation:

136.40 = x + x - 9.50

Simplify:

136.40 = 2x - 9.50

136.40 + 9.50 = 2x

145.90 = 2x

72.95 = x

x = 72.95 (purchase 1)

72.95 - 9.50 = 63.45 (purchase 2)

72.95 + 63.45 = 136.40 (check for truth)

 

 

Answer 2

Answer: 1st purchase=72.95 and 2nd puchase=63.45

 

Solution:

 

To solve this, you need to define the two purchases algebraically. The purchase for which no information is given, we will define as x; therefore, the first purchase is equal to x. The second purchase is 9.50 less than the 1st purchase. Therefore, we define the second purchase as x-9.50. Now we know that the total of the two purchases is equal to 136.40 and therefore we get the following equation:

 

x+(x-9.50)=136.40

2x-9.50=136.40

2x=136.40+9.50

2x=145.90

x=145.90/2

x=72.95; therefore this is the amount of the 1st purchase. By subtracting 9.50 from this amount we get the amount of the second purchase which equals 63.45. 

 

Hope this helps.