The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to $\frac{1}{2}$ .

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4

5n = 3d and 2n - 4 = d - 2

3n = 5d and 2n - 4 = d - 2

Answer:

5n = 3d and 2n – 4 = d – 2

Solution:

Let n be the numerator of the fraction and d be the denominator of the fraction.

Given the numerator and denominator of a fraction are in the ratio of 3 to 5.

This can be written as n : d = 3 : 5.

⇒ $\frac{n}{d}= \frac{3}{5}$ – – – – (1)

Do cross multiplication, we get

⇒ 5n = 3d

When the numerator and denominator are decreased by 2, the fraction is equal to $\frac{1}{2}$ .

⇒ $\frac{n-2}{d-2}= \frac{1}{2}$

Do cross multiplication, we get

⇒ 2(n –2)=1(d – 2)

⇒ 2n – 4 = d – 2

Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.

6 0

4 years ago

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James gets $6 for his weekly allowance and spends $4 of it. His brother Mike gets $7 for his weekly allowance and spends $3 of i

maria [59]

Answer:

$24

Step-by-step explanation:

James

Allowance per week = $6

He spends = $4

Balance = $6 - $4 = $2

Mike

Allowance per week = $7

He spends = $3

Balance = $7 - $3 = $4

Their mother's birthday is in 4 weeks

how much money can they save together in that time to buy her present?

James savings per week × 4 weeks

= $2 × 4

= $8

Mike's savings per week × 4 weeks

= $4 × 4

= $16

Total amount James and Mike can save together = $8 + $16

= $24

6 0

3 years ago