Need Help WIth Algebra Word Problem?

Question

Four tenths of a number increased by the second number equals 19. One tenth of the first number decreased by the second number is equal to 1. What are the two numbers?

Answer 1

y=first #
X=2nd #

4/10y+X=19

1/10y-X=1

this is the part where u solve it...ull nver learn unless u do it urself...sorry but thats all i can do

Answer 2

For a system of two unknowns we need two equations. Conveniently we are given two relations. They are as follows:

Let f be the first number and let s be the second number.

The first equation is:
.4f + s = 19 Four tenths (.4) of (times) the first number (f)increased by (+) the second number (s) is (equal to) nineteen.

The second equation is:
.1f - s = 1 One tenth (.1) of (times) the first number (f) decreased by (-) the second number (s) is (equal to) one.

We take these two equations and add them together:
.4f + s = 19
.1f - s = 1

this gives us:
.5f = 20

Now we divide each side by .5
This gives us:
f = 40

Now we substitute this into one of the equations
.4(40) + s = 19
and solve for s:
16 + s = 19 Subtract 16 from each side.
s = 3

Now we can check this answer by substituting into the other equation:
.1(40) - 3 = 1
4 - 3 = 1 ?
Yes it does..... So we are done.

Answer 3

It's a quadratic equation.

The first number = x
The second number - y

4/10x + y= 19

1/10x - y = 1

Add the two equations together

= 5/10 x = 20

or, 5x = 20x10 = 200

or, x = 200/5 = 40

Since x = 40

Then the first equation becomes

4/10 x 40 + y =19

or, 16 + y = 19

or, y = 19 - 16 = 3

And the second equation;

1/10 x 40 - y = 1

or, 4 - y = 1

but Y has already been seen to be = 3

And it fits.

4 -3 = 1

Therefore,

x = 40

and

y = 3

QED

Answer 4

Let the first number be x and the second number be y

Then (4 * x)/10 + y = 19 (i) and x / 10 - y = 1 (ii)

From (ii), y = (x / 10) - 1

Substitute in (i)

(4 * x)/10 + (x/10) = 20 Add the terms on the left and multiply by 10

5 * x = 200

x = 40 and by (ii) y = 3

Answer 5

don't know but

Theorem: All positive integers are equal.

Proof: Sufficient to show that for any two positive integers, A and B, A = B.

Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.

Proceed by induction.

If N = 1, then A and B, being positive integers, must both be 1. So A = B.

Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.

Answer 6

So there are 2 numbers, call the first one a and the sencond b.
Use the Word problrm to help you set out the equations:
{ / means divided by and * means times }
a / 10 *4 +b = 19
and
a /10 * 1 - b = 1
so a= 40 and b=3

Answer 7

Let first number = x
Let second number = y

You two equations are:

4x/10 + y = 19 and x/10 - y =1

Now from the first equation: y=19-4x/10
And substitute/replace into second equation:
19 - 4x/10 = -1 + x/10
20 = 5 x /10
x=40
Therefore, y = 19-4x/10 = 3

ANSWER
first number = x = 40
second number = y = 3

Answer 8

20

Answer 9

a=40 b=3

Answer 10

The first equation is
0.4x+ y= 19
the second equation is
0.1x -y = 1
now adding these to equations we get
0.4x + y + 0.1x - y = 19+1
simplifying this we get
0.4 x + 0.1 x = 20
0.5 x = 20
therefore x = 20/0.5 = 40
now substitute x = 40 in any one of the two equations
eg: 0.1 (40) - y = 1
4 - y = 1
therefore y = 4-1 = 3.
hence x= 40 and y = 3

hope thats helpful......

Answer 11

this word problem involves "first number"and "second number", so let's use a let statement:
let x=1st number
y=2nd number.

first part: "four tenths of a number increased by second number =19"

4x
--- +y=19
10

to get rid of the fraction, multiply every term by 10 so you get:

4x+10y=190
second part: one tenth of first number decreased by second number is1

1x
---- - y=1
10

get rid of the fraction to make it easier and you have:
1x-10y=10

put the two equations next to each other:
1x-10y=10
4x+10y=190

you see that there is -10y in the first equation and 10y in the second equation. Therefore, we can eliminate the y's and leave only one variable. if we add the second equation to the first, we have:

(1x+4x)+(-10y+10y)=10+190
simplified: 5x=200
x=40

so the first number is 40. plug it back into an equation, and you can find the second number.

for example, if you plugged it back into the equation given in the first part of the equation:

4(40)
------ +y=19
10

4(40)+10y=190

160+10y=190
10y=30
y=3

so first number is 40, second number is 3
(I'm sure of my answer; I checked it)