Claire bought 180 candies and 140 pens for goody bags for her birthday. what is the largest number of goody bags that claire can make so that each goody bag has the same number of candies and the same number of pens?

20

Step-by-step explanation:

Given : Claire bought 180 candies and 140 pens for goody bags for her birthday.

To find : The largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens ( such that no pens or candies left).

So we find the GCF ( Greatest common factor ) or Number of candies and Number of pens.

i.e. we need to find GCF of 180 and 140 .

Prime factorization of 180 =

Prime factorization of 140 =

The greatest common factor of 180 & 140 =

∴ Claire can make 20 goody bags so that each goody bag has the same number of candies and the same number of pens.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3