we know that
Eva needs [tex] \frac{3}{5} [/tex] pound of clay for one piece and [tex] \frac{7}{10} [/tex] pound of clay for the other piece
Step 1
Find the total pound of clay for the two pieces
[tex] \frac{3}{5} +\frac{7}{10} =\frac{(2*3+7)}{10} \\ \\ =\frac{13}{10} pounds [/tex]
Eva has [tex] 3 [/tex] bags of clay that weigh [tex] \frac{4}{5} [/tex] pounds each.
Step 2
Find the total weigh of the [tex] 3 [/tex] bags of clay
[tex] 3*\frac{4}{5} =\frac{12}{5} pounds [/tex]
Part a ) How many bags of clay will Eva need to make both pieces of pottery?
by using proportion
[tex] \frac{1}{\frac{4}{5}} =\frac{x}{\frac{13}{10}} \\ \\ \frac{13}{10} =\frac{4}{5} x\\ \\ x=\frac{5*13}{4*10} \\ \\ x=\frac{65}{40} \\ \\ x=1.625bags [/tex]
therefore
the answer Part a)
she needs [tex] 2 [/tex] bags
Part b) How many pounds of clay will she have left?
Calculate the total weigh of the [tex] 3 [/tex] bags of clay minus the total pound of clay for the two pieces
so
[tex] \frac{12}{5} -\frac{13}{10} =\frac{(2*12-13)}{10} \\ \\ =\frac{(24-13)}{10} \\ \\ =\frac{11}{10} \\ \\ =1\frac{1}{10} pounds [/tex]
therefore
the answer Part b) is
[tex] 1\frac{1}{10} pounds [/tex]
