Question 181512
a picture frame made of wooden pieces that are 7 centimeters and 3 centimeters
 in length. He needs 20 pieces, and the total perimeter of the frame needs to
 be 108 centimeters. If Giao cuts eight 3 centimeter pieces first and is left 
with 0.8 meter of wood, will he have enough wood to cut the 7 centimeter pieces?
:
Find the no. of pieces of each required:
Let x = no. of 7 cm pieces
Let y = no. of 3 cm pieces
:
The total no. of pieces equation:
x + y = 20
y = (20-x); for substitution
:
The total length of these pieces:
7x + 3y = 108
:
Substitute (20-x) for y
7x + 3(20-x) = 108
;
7x + 60 - 3x = 108
:
7x - 3x = 108 - 60
:
4x = 48
x = {{{48/4}}}
x = 12 ea 7 cm pieces
then
20 - 12 = 8 ea 3 cm pieces
:
"left with .8 m, will he have enough wood to cut the 7 centimeter pieces?"
:
.8 m = 80 cm
:
80 - (12 * 7) = 
80 - 84 = -4, obviously, he won't