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Number Problem
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Number Problem


(Philippines)







































1. One number is less than five times another. If their sum is 70, what the smaller number? complete solution.
2. The smallest ofteh numbers is one-third of the largst numberand the second number is one-half the largest number. If their sum is 44?
WITH COMPLETE SOLUTION

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Dec 09, 2011
Number Problem
by: Staff


Question:

(Philippines)

1. One number is less than five times another. If their sum is 70, what the smaller number? complete solution.
2. The smallest ofteh numbers is one-third of the largst numberand the second number is one-half the largest number. If their sum is 44?
WITH COMPLETE SOLUTION




Answer:

1. first problem


x = first number

y = second number

One number is less than five times another.

x < 5y

their sum is 70

x + y = 70

-----------------------------------
x + y = 70


x + y - y = 70 - y

x + 0 = 70 - y

x = 70 - y

y = 70 - x



x < 5y

70 - y < 5y

70 - y + y < 5y + y

70 + 0 < 6y


70 < 6y

70/6 < 6y/6

70/6 < y

35/2 < y

17.5 < y



x < 5*(70 - x)

x < 350 - 5x

x + 5x < 350 - 5x + 5x

6x < 350 + 0

6x < 350

6x/6 < 350/6

x < 175/3

x < 58.3333

y > 17.5


the final answer is:

when y = 35, x also = 35. At this point both x and y are equal.

When y < 35, x is the larger number (y is the smaller number)

When y > 35, x is the smaller number (y is the larger number)



2.


The smallest of the numbers is one-third of the largest number

x = (1/3) * z


second number is one-half the largest number

y = (1/2) * z


their sum is 44

x + y + z = 44

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

x + y + z = 44

(1/3) * z + (1/2) * z + z = 44

(2/6) * z + (3/6) * z + (6/6) * z = 44

(11/6) * z = 44

(6/11) * (11/6) * z = (6/11) * 44

(11/11) * (6/6) * z = (6/11) * 44

(1) * (1) * z = (6/11) * 44

z = (6/11) * 44

z = 24


x = (1/3) * z

x = (1/3) * 24

x = 8


y = (1/2) * z
y = (1/2) * 24

y = 12


the final answer is: x = 8, y = 12, z = 24




Thanks for writing.

Staff
www.solving-math-problems.com



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