Equations, Inequalities, & VIC's ch. 7

[dl]

Hi, i have a question on the problem set, #6

Mr. and Ms. Wiley have a chiled every J years. Their oldest is now T years old. If they have a child 2 years from now, how many children will they have in total?

The answer is A, (T+2)/J +1

First issue i had was that didnt know that they had their first child at time zero. So that threw my count off, so will actual test questions be a little more clear and less ambiguous?

2nd issue is that the numbers i chose, after knowing that they have a child at time zero turns out to be a fraction and the closest answer could be if you round up in some cases and other cases it will be off. Here are 2 examples

J = 10
T = 20

3 children total (1 age 0 just born, 2nd age 10, 3rd age 20) plus child in 2 years equals 4 children total.

(20+2)/10 + 1 = 3.2 children this answer when rounded equals 3

2nd set i chose was

J = 4
T = 12

So children are ages 0, 4, 8, 12, then child in 2 years is 5 children total

(12+2)/4 +1 = 4.5 children, could possibly work as answer A if you round up.

am i going crazy here?

Thanks

(12+2)/4 +1 =

[Guest]

just one more thing to add, is that it seems the answer only works with the MGMAT numbers chosen where

J = 2
T = 12

[RonPurewal]

First issue i had was that didnt know that they had their first child at time zero. So that threw my count off, so will actual test questions be a little more clear and less ambiguous?

this question concerns the age of children. there is no possible way for a child to be born at any age other than zero,** so the problem need not mention the 'starting age'.

2nd issue is that the numbers i chose, after knowing that they have a child at time zero turns out to be a fraction and the closest answer could be if you round up in some cases and other cases it will be off. Here are 2 examples

J = 10
T = 20

3 children total (1 age 0 just born, 2nd age 10, 3rd age 20) plus child in 2 years equals 4 children total.

can't do that.

the problem statement - every J years - implies that the family has children at regular intervals of J years. if you choose J = 10, then, that means that the family has a child once every ten years, exactly. therefore, if the youngest child is newborn, then you can't satisfy the conditions of the problem: the next child, if there is one, won't come for another ten years (not 2 as stipulated in the problem).

2nd set i chose was

J = 4
T = 12

So children are ages 0, 4, 8, 12, then child in 2 years is 5 children total

same issue.

--

you can pick other sets of numbers, but you have to pick them so that they can have a child in 2 years without violating the regular intervals they've already established. the easiest way to figure this out is to say that the baby coming next is negative two years old, and then count up from there.

for instance:

let's say you want J to be 10, as in your first example.
then the baby about to be born is -2 years old ... so the existing children are 8 and 18. (you could also have 28 and 38 and ..., but human fertility has its limits.)
so let's have J = 10 and T = 18.
then, including the baby to be born in two years, there will be 3 children.
(T + 2)/J + 1 = 20/10 + 1 = 3

--

i'll leave your other example as an exercise for you; try to figure out some ages that will work if you let J = 4 years.

[Guest]

2nd issue is that the numbers i chose, after knowing that they have a child at time zero turns out to be a fraction and the closest answer could be if you round up in some cases and other cases it will be off. Here are 2 examples

J = 10
T = 20

3 children total (1 age 0 just born, 2nd age 10, 3rd age 20) plus child in 2 years equals 4 children total.

can't do that.

the problem statement - every J years - implies that the family has children at regular intervals of J years. if you choose J = 10, then, that means that the family has a child once every ten years, exactly. therefore, if the youngest child is newborn, then you can't satisfy the conditions of the problem: the next child, if there is one, won't come for another ten years (not 2 as stipulated in the problem).

2nd set i chose was

J = 4
T = 12

So children are ages 0, 4, 8, 12, then child in 2 years is 5 children total

same issue.

--

you can pick other sets of numbers, but you have to pick them so that they can have a child in 2 years without violating the regular intervals they've already established. the easiest way to figure this out is to say that the baby coming next is negative two years old, and then count up from there.

for instance:

let's say you want J to be 10, as in your first example.
then the baby about to be born is -2 years old ... so the existing children are 8 and 18. (you could also have 28 and 38 and ..., but human fertility has its limits.)
so let's have J = 10 and T = 18.
then, including the baby to be born in two years, there will be 3 children.
(T + 2)/J + 1 = 20/10 + 1 = 3

--

i'll leave your other example as an exercise for you; try to figure out some ages that will work if you let J = 4 years.

thanks for answering. i'm still confused about this part: if we say -2, 8, 18 as the ages, how is the next baby being born in 2 years following the stipulation of the 10 years.

[StaceyKoprince]

The stipulation of the 10 years is that the children are 10 years apart. The "-2" child is 10 years younger than the 8 year old child, who is 10 years younger than the 18 year old child.

One baby is being born in 2 years and it has been 8 years already since the last one was born. 8+2=10 years between kids.