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Question

Dionne has six steel balls of equal mass. If she puts five of them in one pan of a beam balance and one ball and a 100 g mass in the other pan, the pans balance each other. What is the mass of each steel ball ?

and also.

the sum of two integers is 15. Three times one of the numbers is 11 less than 5 times the other. find the numbers.


step by step instructions please.
thank you greatly <3

Answer 1

1) let mass of each ball be m.
Then,
5 * m = m +100g since 5 balls in one pan balance one ball + 100g mass in the other pan

Then, the equation is:
5m - m = 100
4m = 100
m = 25g -> mass of each ball

2) let integers be x and y

given that x + y = 15
and 3x+11 = 5y ... 4 times x is 11 less than 5 times y

Subtracting three times first equation from second equation:

3x + 11 - 3x - 3y = 5y - 45
11 - 3y = 5y - 45
56 = 8y
y = 7
That implies x = 15-y = 15-7 = 8

Therefore, the two integers are 7 and 8.

Answer 2

one ball and 100gm is equal to 5 balls.Therefore, 4 balls weigh 100 gm. So mass of one ball=100/4=25.g Second question. let the first number be x.Therefore,the second number is 15-x. Now according to the problem 3x=5(15-x) - 11 =. 3x=75-5x-11 => 3x+5x=64 => 8x=64. Therefore,the first number is 8 and the second number is 15-8 or 7 ans

Answer 3

first question:
let each ball be of mass X then the equation of left side of the pan is 5X ( five balls on one side) and the right side is X+100 ( one ball +100 grams) as this must be equal to balance then:
5x=x+100
4x=100 (taking x of RHS to LHS)
x=25 grams

second question:
let one integer be x other be y then:
x+y = 15 -----------(1)
and from 2nd part
5y-3x= 11 ----------(2)
multiply eqn(1) by 3 and add new equation with (2)
you get 8y=56 or y=7
so from (1) you get x=8

(you must read your linear equations chapter many times cause this is basic stuff)

Answer 4

i'm very young

Answer 5

$1.98