Aaliyah’s pens to Mariah’s pens ratio was 2:3, but after getting 16 more pens to Aaliyah from her dad, the ratio became 2:1. We need to find out how many pens Mariah had. Also, if Mariah gave away six pens, what would be the new ratio of Aaliyah’s pens to Mariah’s pens?

Consider x for the unknown number of pens

The ratio of the number of Aaliyah’s pens to the number of Mariah’s pens is

2x : 3x

After getting 16 pens from Dad, the ratio between Aaliyah’s pens to the number of Mariah’s pens becomes 2 : 1

⇒ (2x + 16) : 3x = 2 : 1

⇒ \$(2x + 16)/(3x) = 2/1\$

After cross multiplication, we get

⇒ 2x + 16 = \$2 times 3x\$

⇒ 2x + 16 = 6x

Move the x coefficient to right side

⇒ 16 = 6x - 2x

⇒ 16 = 4x

Divide 4 on both sides we get

⇒ \$16/4 = (4x)/4\$

⇒ 4 = x

Substitute x value in ratio we got individual pens of Aaliyah and Mariah

⇒ \$2 times 4 = 8 "pens"\$

⇒ \$3 times 4 = 12 "pens"\$

After that Aaliyah got 16 pens and Mariah gave away 6 pens ,the Aaliyah have 24 pens and Mariah have 6 pens

⇒ 8 + 16 = 24 pens

⇒ 12 - 6 = 6 pens

Now the present ratio is

⇒ 24 : 6

After simplification, we get

⇒ \$ \cancel24^4:\cancel6^1\$

⇒ 4 : 1

Finally Aaliyah’s having 12 pens and the ratio is 4 : 1

Answer

D