Harriet works at the Mint, where new coins are made. Old and fake coins are also destroyed there. Harriet has 10 bags of $1 coins. All 10 bags contain the same number of coins. Harriet knows that nine bags contain only good coins and that one bag contains only fake coins. The fake coins are all about 0.5 gram short. Harriet has forgotten which bag contains the fake coins. Harriet has a set of scales for weighing like the ones in the illustration. What is the lowest number of times she can weigh bags on the scales in order to find the bag of fake coins?

3 times

Step-by-step explanation:

She would have to weigh the fake coins and another bag of real coins to spot a difference, and then she would need to check another bag to see which was correct. Maybe thats right.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form