Evaluating Expressions with Fractions

Question

20 feet of ribbon, cutting ribbon into 7 1/2 inch or 6 3/4 inch lengths to make bracelets. Write an algebraic expression tha can be use to figure out how many bracelets can be made.

How can you change above expression if you want to figure out how many feet of ribbon needed to make 100 bracelets?

Answer 1

20 feet = 240 inches

240 = (15/2) x + (27/4) y where x is the larger and y is the smaller bracelet

multiplies by 4:

960 = 30x + 27y

-30x + 960 = 27y

(-30/27)x + (960/27) = y

(-10/9)x + (320/9) = y <-- tell you how many small bracelets can be made

given the # of larger bracelets

For example: x=9 large bracelets, (-10/9)(9) + 320/9 =

-10 + 320/9 =

(-90+320)/9 =

230/9 =

= 25 small bracelets with 5 inches left

On the other hand: 960 = 30x + 27y

960 - 27y = 30x

960/30 - 27/30 y = x

32 - (9/10)y = x

is the formula for determining the # of large bracelets

that can be made given the # of small bracelets

for 100 feet, you do the problem the same way, except 100ft = 1200 inches,

so the original equation is 1200 = (15/2) x + (27/4) y