Helene bought a ring and a handbag at discounted prices during a sale. The total discount given for the two items was $1946.60. She was given a 25% discount for the ring. She spent a total of $1940.40 on these two items. She spent $458.40 less on the ring than on the handbag. What was the percentage discount given for the handbag?

The percentage discount given for the handbag is 90.48%.

Step-by-step explanation:

From the question, the following can be obtained:

D = Total discount on the two items = $1946.60

T = Total amount spent on the two items = $1940.40

r = Percentage discount given for the ring = 25%, or 0.25

h = Percentage discount given for the handbag = ?

H = Amount spent on the handbag = ?

Since Helene spent $458.40 less on the ring than on the handbag, therefore we have:

R = Amount spent on the ring = H - $458.40

From the above, we have:

T = H + R

T = H + H - $458.40

T = 2H - $458.40 …………………… (1)

Substituting T = $1940.40 into equation (1) and solve for H, we have:

$1940.40 = 2H - $458.40

$1940.40 + $458.40 = 2H

$2,398.80 = 2H

H = $2,398.80 / 2

H = $1,199.40

Since,

R = H - $458.40 ……………………. (2)

By substituting H = $1,199.40 into equation (2), we have:

R = $1,199.40 - $458.40

R = $741

Amount of discount on ring = r * R = 25% * $741 = $185.25

Amount of discount on handbag = D - Amount of discount on ring = $1946.60 - $185.25 = $1,761.35

h = Amount of discount on handbag / H = $1,761.35 / $1,199.40 = 0.90483406965992, or 90.483406965992%

Rounding to 2 decimal places, we have:

h = 90.48%

Therefore, the percentage discount given for the handbag is 90.48%.