Lina wanted to buy a bag. she saw a red bag on sale at 15% discount and a blue bag at 20% discount. both bags had the same original price before the discounts. to buy the red bag, lina would need $2.50 more than what she had. so lina bought the blue bag. after that, she had $2 left. (a) what was the original price of the red bag? (b) how much money did lina have at first?

a) The original price of the bag was $90

b) Lina was having $74

Step-by-step explanation:

Let the original price of  the bags be 'x'

and,

the money Lina had be 'y'

then according to the question

Price of red bag after 15% discount = x - 0.15x = 0.85x

Price of red bag after 20% discount = x - 0.20x = 0.80x

also,

0.85x = y + $2.5 (1)

0.80x = y - $2  (2)

subtracting the equation (2) from  (1), we get

    0.85x = y + $2.5

- ( 0.80x = y - $2   )

      0.05x = $4.5

or

x = $90

a) The original price of the bag was $90

b) on substituting the value of x in the equation (1), we get

0.85 × 90 = y + $2.5

or

76.5 = y + $2.5

or

y = $74

Hence, Lina was having $74

∠cbe and ∠deb are same-side interior angles.

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