Answer:
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%.
