The store pays $2 for each Blu-ray disc, $0.75 for each DVD, and
$0.1 for each VHS cassette
Step-by-step explanation:
An electronics store buys media from customers to resell.
The given is:
1. The store pays one customer $5.30 for one Blu-ray disc, four DVDs,
and three VHS cassettes
2. The store pays the second customer $11.50 for five Blu-ray discs
and two DVDs
3. The store pays the third customer $10.20 for two Blu-
ray discs, eight
DVDs, and two VHS cassettes
We need to find the amount the store pays for each item
Assume that:
The cost of a Blue-ray disc is $x
The cost of a DVD is $y
The cost of a VHS cassette is $z
∴ x + 4y + 3z = 5.3 ⇒ (1)
∴ 5x + 2y = 11.5 ⇒ (2)
∴ 2x + 8y + 2z = 10.2 ⇒ ÷ 2
∴ x + 4y + z = 5.1 ⇒ (3)
- Subtract equation (3) from equation (1)
∵ x + 4y + 3z = 5.3 ⇒ (1)
∵ x + 4y + z = 5.1 ⇒ (3)
∴ 2z = 0.2
- Divide both sides by 2
∴ z = 0.1
Substitute the value of z in equation (3)
∴ x + 4y + 0.1 = 5.1
- Subtract 0.1 from both sides
∴ x + 4y = 5 ⇒ (4)
Let us solve equations (2) and (4)
∵ 5x + 2y = 11.5 ⇒ (2)
∵ x + 4y = 5 ⇒ (4)
- Multiply equation (2) by -2 to eliminate y
∴ -10x - 4y = -23 ⇒ (5)
- Add equations (4) and (5)
∴ -9x = -18
- Divide both sides by -9
∴ x = 2
- Substitute the value of x in equation (2)
∴ 5(2) + 2y = 11.5
∴ 10 + 2y = 11.5
- Subtract 10 from both sides
∴ 2y = 1.5
- Divide both sides by 2
∴ y = 0.75
The store pays $2 for each Blu-ray disc, $0.75 for each DVD, and
$0.1 for each VHS cassette
Learn more:
You can learn more about solving equations in brainly.com/question/9045597
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