Algebra Word Problem?

Question

a.) Seperate 66 into two parts so that 2/5 of one part exceeds 5/8 of the other part by 10. Find the two numbers.

b.) One side of a rectangle exceeds three times the other side by two. Find the lengths of the three sides if the perimeter is 36.

Can you help me with this???
I am very confused trying to find out the solution for this one.
Please include the full solution of the problem in your answer.
Thanks in advance!!!

Answer 1

a.) Seperate 66 into two parts so that 2/5 of one part exceeds 5/8 of the other part by 10. Find the two numbers.............................EXCEEDS means EQUAL if you ADD something

P1 = X

P2 = 66 - X



(2/5)(X) = (5/8)(66 - X) + 10...................Multiply all three terms by common denominator of 40



40*(2/5)(X) = 40*(5/8)(66 - X) + 40*10



16X = 25(66 - X) + 400



16X = 1650 - 25X + 400



41X = 2050



X = 50



66 - X = 66 - 50 = 16



P1 = 50

P2 = 16..............ANSWERS







b.) One side of a rectangle exceeds three times the other side by two. Find the lengths of the three( YOU MEANT TWO I HOPE) sides if the perimeter is 36.



W = X

L = 3X + 2



2L + 2W = P



2(3X + 2) + 2(X) = 36



6X + 4 + 2X = 36



8X = 32



X = 4



3X + 2 = 3*4 + 2 = 12 + 2 = 14



W = 4

L = 14.................ANSWERS

Answer 2

a. This is just asking to find two variables that add up to 66, with boundary conditions. So, start by saying that 66 = x + y, and then impose the boundary conditions on x and y in a separate equation:

(2/5)*x = (5/8)*y + 10. In words, this equation says "Two fifths of x is ten more than 5/8ths of y", which is the same as your problem. From here, you just need to solve the second equation for x (or y), plug it into the first equation (66 = x + y), and then get the other variable.



b. This is very similar. All we need to do is find the two equations that control this system. Remember that a rectangle's perimeter is L + W + L + W = P, or 2L + 2W = P, where P is the perimeter, W is the width, and L is the length. The two equations you have here are that 2L + 2W = 36, and that L = 3W + 2. Here, just plug the L in the second equation into the first equation directly to find W, and use that W to find L.



I think the problem here is the wording, "Exceeds by ____". That threw me for a second too, but if you just think about it, you can see what it means. For example, if I were to say "X exceeds 5 by 3", you would know that X is 8. You can write this algebraically as "X = 5 + 3".

Answer 3

a) Let the two numbers be x and y.

1) x + y = 66 or y = 66 - x

2) (2/5)x = (5/8)y + 10

substitute eq(1) into eq(2):

(2/5)x = (5/8)(66 - x) + 10

2x/5 = 330/8 - 5x/8 + 10

put into common denominator:

16x/40 = 1650/40 - 25x/40 + 400/40

16x = 1650 - 25x + 400

41x = 2050

x = 2050/41 = 50

using eq(1):

y = 66 - 50 = 16

check:

2(50)/5 = 5(16)/8 + 10

20 = 20

x = 50, y = 16



b) Let one side be x, the other y. I assume that you want two sides rather than 3.

1) x = 3y + 2

2) 2x + 2y = 36

substitute eq(1) into eq(2):

2(3y + 2) + 2y = 36

6y + 4 + 2y = 36

8y = 32

y = 32/8 = 4

using eq(1):

x = 3(4) + 2 = 14

check using eq(2):

2(14) + 2(4) = 36

36 = 36

One side is 14, the other is 4.



- .--

Answer 4

1) let the 2 parts be n and 66-n. Then (2/5)n = (5/8)(66-n)+10

16n=25(66-n) + 400

16n = 1650-25n+400

41n = 2050

n=50

66-n = 16



2) not sure what "Find the lengths of the three sides" means - - there are 4 sides to a rectangle (2 pairs of equal sides). Ignoring that, we have:



L=3W + 2



2L +2W = 2(3W+2) + 2W = 8W + 4 = 36



8W = 32

W=4

L=14

Answer 5

One part—x:

2/5x - 5/8(66 - x) = 10 (multiply both sides by 40 to eliminate fractions)

16x - 25(66 - x) = 400

16x - 1,650 + 25x = 400

41x = 2,050

x = 50



The other part:

= 66 - 50

= 16



Answer a.): 50 and 16 are the numbers.

----------------

Shorter side—x:

2(x + 3x + 2) = 36

4x + 2 = 18

4x = 16

x = 4



Longer side:

= 3(4) + 2

= 12 + 2

= 14



Answer b.): 4 & 14 are the lengths of the sides.

Answer 6

a) let the numbers be x and y.

now x+y=66;

and (2/5)*x -(5/8)*y=10;

solve the two equations to obtain the answer..

b)let the sides be a and b.

2(a+b)=36;

and a-3b=2;

solve the two equations...

you should remember one thing..

if it is given that one thing exceeds other by this much amount then the meaning is the difference between them is given ....