MAth word problem..10 points?

Question

Can u slove this word problem equation

The sum of two numbers is 39. Twice the first number plus 3 times the second number is 101.

a) Find the numbers using guess and check
b) Find the numbers by writing and solving an equation.

c) Which method do you pefer?Why?

Answer 1

a 16 and 23

b
2x+3y=101
x+y=39
x=39-y
2(39-y)+3y=101
78-2y+3y=101
y=23
x=16

i like the first one better, its more fun

Answer 2

a) using guess and check really gets you nowhere. you just randomly choose numbers and hope you guess it correctly.

b) sum of two numbers is 39
sum means addition, so if we add two numbers we should get 39
we can say x is the first number and y is the second number

x + y = 39

twice the first number plus 3 times the second number is 101
twice the first number can be written as 2x
3 times the second number can be written as 3y
so now we have
2x + 3y = 101

now we have two equations to work with
x + y = 39
2x + 3y = 101

if we use substitution, we can solve for either x or y in the first equation. if we choose to solve for x, you would follow these steps.
x + y = 39
subtract y from both sides
x = 39 - y

now we can substitute x in the second equation with 39 -y
2 (39 - y) + 3y = 101
distribute
78 - 2y + 3y = 101
combine like terms
78 + y = 101
subtract 78 from both sides
y = 23

now we can substitute y = 23 into the first problem to solve for x
x + y = 39
x + 23 = 39
subtract 23 from both sides
x = 16
y = 23

c) i prefer to use writing and solving an equation. there's no need to throwing out numbers out there to see which one is correct.

Answer 3

I'd rather not use the guess and check method (since there's nothing mathematical about it), so I'll just write the equation.

If we let x be one of the numbers, it would follow that (39 - x) is the second number.

Twice the first number (i.e. 2x) and 3 times the second number (i.e. 3(39 - x)) is 101. That means

2x + 3(39 - x) = 101

Solving this algebraically,

2x + 117 - 3x = 101
-x = -16
x = 16

Since x = 16, the other number is (39 - 16) = 23.

Answer 4

Let the two numbers be x and y.

Then we have

x + y = 39
2x + 3y = 101

Subtracting twice the first equation from the second

y = 101 - 2*39 = 101 - 78 = 23
x = 39 - y = 39 - 23 = 16

The two numbers are 16 and 23.

An equation is much preferable to "guess and check". It is quicker, easier, and more reliable.

Answer 5

a) guess and check. well, I guess that the first is 16 and the second is 23. Two times the first is 32, plus three times the second is 69, and yes that adds up to 101. hurray. my guess was right.

b) x + y = 39 --> y = 39 - x
2x + 3 y = 101
2x + 3 (39-x) = 101
2x -3x + 117 = 101.
-x = -16
x = 16.
16 + y = 39
y = 23.

so that's x = 16 and y = 23.

c) i like B. because I said so

Answer 6

I prefer (b) method, cause it takes 99% confirmation to get the right answer, while (a) method takes alot lesser chance to answer correctly. Also it takes longer time

x+y=39
x=39-y

2x+3y=101
2x=101-3y
x=(101-3y)/2

39-y=(101-3y)/2
2(39-y)=101-3y
78-2y=101-3y
3y-2y=101-78
y=23

x+y=39
x=39-y
x=39-23
x=16

Answer 7

i prefer methob b

c) x+y=39
2x+3y=101

x= 39-y

2(39-y)+3y=101
78-2y+3y=101
y= 23

x= 16

Answer 8

try 25 and 14
goes under
try 23and 16
fits in
sum=39
2x+3y=101
x+y=39
2x+2y=78
y=23
x=16
better method is the latter
because it is sure shot and faster