Question #d071b

2 Answers
Dec 17, 2017

They will each have 120 stamps at the end of 4 months.

Explanation:

So, based on this, you can write two equations:
56+16x=y
72+12x=y

We know that they both have to equal the same thing after the same amount of months, after all. So, we can eliminate one of the variables like this:
-(56+16x=y)
color(white)(....)72+12x=y

Leading to:
-56-16x=-y
color(white)(. . )72+12x= y

Then you just add down, and you're left with:
16-4x=0

From there, you solve for x, and you can find out that x=4, which is how many months it will take.

Plug 4 into one of the first equations, and you've found your y.
56+16(4)=y
56+64=y
120=y

You can do both to check.
72+12(4)=y
72+48=y
120=y

Dec 17, 2017

In 4 months, Kai and Xian will each have 120 stamps.

Explanation:

The situation of each collector can be written as a linear equation.

Xian
Xian gets 16 stamps per month for x months, plus a starting number of 56 stamps.

That is a linear equation
y = mx + b

y = Xian's total stamps
m = the number received per month
x = the number of months
b = the number of stamps to start

y =  m  x +  b
y = 16 x  + 56
~ ~ ~ ~ ~ ~ ~ ~ ~

Kai
Kai gets 12 stamps per month, plus a starting number of 72 stamps.

y =  m x  +  b
y = 12  x  + 72
~ ~ ~ ~ ~ ~ ~ ~

The problem wants to know how many months until they have an equal number of stamps, so set the equations equal to each other and solve for x, already defined as "the number of months."

16 x + 56 = 12 x + 72
solve for x, already defined as "the number of months when they will be equal."

1) Subtract 12x from both sides to get all the x terms together
4x + 56 = 72

2) Subtract 56 from both sides to isolate the 4x term
4x = 16

3) Divide both sides by 4 to isolate x, already defined as "the number of months"
x = 4 larr answer for "the number of months until they own an equal number of stamps"
~ ~ ~ ~ ~ ~ ~ ~

To find how many stamps they will each own in 4 months, sub in 4 for x in the equations

Xian
Xian already has 56 stamps, and will receive 16 a month for 4 months.

Xian: 16 (4) + 56
color(white)(..........)64   + 56
color(white)(..............)120 stamps after 4 months

Kai
Kai already has 72 stamps and will receive 12 a month for 4 months.

Kai: 12 (4) +  72
color(white)(.......)48    +  72
color(white)(.............)120 stamps after 4 months

~ ~ ~ ~ ~ ~ ~

Answer:
In 4 months, Kai and Xian will each have 120 stamps.