Question

The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?'a) 20b) 30c) 40d) 60e) 90

Answer 1

Answer:  c) 40

Step-by-step explanation:

Given : The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively.

Let the initial number of stamps Kaye and Alberto have are 5x and 3x respectively.

After Kaye gave Alberto 10 of her stamps, the number of stamps Kaye left with = 5x-10   (1)

And Alberto will have 3x+10 stamps.   (2)

Also,the ratio of the number Kaye had to the number Alberto had was 7 : 5.

$\Rightarrow\ \dfrac{5x-10}{3x+10}=\dfrac{7}{5}\\\\\Rightarrow\ 5(5x-10)=7(3x+10)\\\\\Rightarrow\ 25x-50=21x+70\\\\\Rightarrow\ 25x-21x=70+50\\\\\Rightarrow\ 4x=120\\\\\Rightarrow\ x=\dfrac{120}{4}=30$

Now,  As a result of this gift, Kaye will left with= 5(30)-10=150-10=140   stamps.     (from (1))

Albert have now ,3(30)+10=90+10=100 stamps     (from (2))

The number of stamps Kaye has more than Alberto = 140-100=40

Hence, option (c) is the correct answer.