Acarpenter has several boards of equal length, he cuts 3/5 of of each board. after cutting the boards the carpenter notices that he has enough left over to make up the same length as 4 of the original boards. how many boards did the carpenter start with?

4 of the original boards have a summed length of 20 units. 5 x 4 = 20.
Since 2/5 is left from each board, you simply add them until the 2's add to 20.So, 2 x 10 = 20. Hence, there are 10 2/5 boards.That's just 4 of the boards that the 2/5 make up, but that should also mean that there are 10 3/5 boards as well.

30/5 + 20/5 = 50/5
Reduction = 10

The carpenter started with 10 5/5 boards.

Assign variables for unknowns.

Let A be the number of pounds of Type A coffee.

Let B be the number of pounds of Type B coffee.

A + B = 150 ( the total weight of the lend of Type A and Type B).

If one pound of Type A costs $4.15 then A pounds costs 4.15A

If one pound of Type B costs $5.60 then B pounds costs 5.6B

4.15A + 5.6B = 712.40  ( total cost of the blend)

At this point you have two equations with A and B as variables.  You can use substitution or elimination method to solve for A.  

A + B = 150

4.15A + 5.6B =  712.40

Substitution method:

A = 150 - B

4.15(150 - B) +  5.6B = 712.40

622.5 - 4.15B + 5.6B = 712.4

622.5 + 1.45B = 712.4

1.45B = 712.4 - 622.5

1.45B = 89.9

B = 89.9/1.45

B = 62

A = 150 - B

A = 150 - 62

A = 88

ANSWER: Elsa used 88 pounds of Type A blend.

Step-by-step explanation:

Assign variables for unknowns.

Let A be the number of pounds of Type A coffee.

Let B be the number of pounds of Type B coffee.

A + B = 150 ( the total weight of the lend of Type A and Type B).

If one pound of Type A costs $4.15 then A pounds costs 4.15A

If one pound of Type B costs $5.60 then B pounds costs 5.6B

4.15A + 5.6B = 712.40  ( total cost of the blend)

At this point you have two equations with A and B as variables.  You can use substitution or elimination method to solve for A.  

A + B = 150

4.15A + 5.6B =  712.40

Substitution method:

A = 150 - B

4.15(150 - B) +  5.6B = 712.40

622.5 - 4.15B + 5.6B = 712.4

622.5 + 1.45B = 712.4

1.45B = 712.4 - 622.5

1.45B = 89.9

B = 89.9/1.45

B = 62

A = 150 - B

A = 150 - 62

A = 88

ANSWER: Elsa used 88 pounds of Type A blend.