Easy PS but confusing translation words

[TRANGZON]

A kernel house 7 times as many mixed-breed dogs as purebred dogs. The ratio of purebred dogs to the total population in the kernel is:
a. 1 to 6
b. 1 to 7
c. 1 to 8
d. 6 to 7
e. 7 to 8

I know it is easy problem but I'm just confused the popular phrase "7 times as many mixed-breed dogs as purebred dogs".

The other same problem is

There are twice as much as English major as history major and three times as many as English majors as mathematics major.
What is the ratio of the number of history major to the number of math major?
a. 6 to 7
b 3 to 2
c. 2 to 5
d. 1 to 5
e. 1 to 6

Iam not Eng native. So, please help me understand.

[sudhir3127]

Use arithemetic .

let the number of purebred dogs be 1

number of mixed-breed dog is 7 times.. which mean 7

total number of dogs 1+7 =8

the ratio of purebred dogs to the total population is 1:8

[AleksandrM]

Whenever a problem tells you that there are X as many Z as Y, then the translation would be in the form

Z = XY

For example, there are twice as many dogs as cats.

Dogs = 2 x Cats

[anksanks]

7 times as many means… for every purebred dog, there are 7 mixed breed ones.
=> if no. of purebred dog = x, there are 7* x mixed breed ones.
=>total dogs = purebred+ mixed breed = x + 7x = 8x
Ratio of pure breed to total dogs = x / 8x = 1/8

Let E= English major, H = history, M = mathematics.
1E=2H – English major – twice of history major
1E=3M – English major = three times mathematics one
=>1E = 2H = 3M
=> H/M = 3/2

[TRANGZON]

Thank everyone for your replies. I clearly understand this problem.