Question

Andrew bought 3 baseball cards for $240. After a few months, he got an offer from his friend Jack to buy the first card for double its original value, along with either the second or third card. Andrew decided to sell the first card (at double its original value) along with the second card (at its original price) and got $320 for it. Or, selling the first card (at double its original value) card along with the third card (at its original price) would have only got him $280. What were the original prices for each of the 3 baseball cards?

A-(80, 120, 40)

B-(80, 130, 30)

C-(130, 90, 20)

D-(120, 80, 40)

Answer 1

The Answer is D. Its actually really simple if you add up the answer chouices

Answer 2

Option D. (120, 80, 40)

Explanation:

Let the cost of 3 baseball cards bought by Andrew are $x, $y and $z.

Now we will form the equations to find the unknown values of x, y, and z.

Statement 1 - Andrew bought 3 baseball cards for $240

Equation will be (x + y + z) = 240 --------(1)

Statement 2 - Jack offered a deal to buy the first card for the double of its original value along with the second card for $320.

Equation will be 2x + y = 320 --------(2)

Statement 3 - Jack offered another deal to buy first card for the double of its original value along with third card for $280

Equation formed 2x + z = 280 ------(3)

Now we can solve these equations to get the values of x, y and z.

From equation 2

y = 320 - 2x

From equation 3

z = 280 - 2x

Now we can replace the values of y and z in equation number 1.

Equation 1 becomes after substitution of y and z values

x + (320 - 2x) + (280 - 2x) = 240

Now we will group the similar terms

(x - 2x - 2x) + (320 + 280) = 240

-3x + 600 = 240

-3x = 240 - 600

-3x = - 360

x =
`(360)/(3)`

x = 120

Now we put x = 120 in the value of y

y = 320 - 2x

y = 320 - 2×120

= 320 - 240

= 80

Similarly we put the value x = 120 in value of z

z = 280 - 2x

= 280 - 2×120

= 280 - 240

= 40

So the original values of 3 baseball cards are (120, 80, 40)

Option D. will be the answer.