Pastries made out of filo dough are brushed with either olive oil or butter (but not both). pastries made out of shortcrust dough are not brushed with anything.

rashid and mikhail submitted a total of x pastries to a baking competition. mikhail used filo dough for all of his pastries, rashid used shortcrust dough for all of his pastries, and each pastry was made using only one kind of dough.

if rashid made 2/3 as many pastries as mikhail, and 5/8 of the filo dough pastries were brushed with olive oil, then how many of the pastries submitted by rashid and mikhail, in terms of x, were brushed with butter?

a) 3x/20
b) 9x/40
c) 1x/4
d) 3x/8
e) 5x/12

3X/20 (option a) of the pastries submitted by Rashid and Mikhail were brushed with butter

Step-by-step explanation:

Rashid pastries (R)

Mikhail pastries (M)

Rashid and Mikhail submitted a total of x pastries

R+M=x (I)

Rashid made 2/3 as many pastries as Mikhail

(2/3)*R=M (II)

Using II in I

R+(2/3)*R=x

(5/3)*R = x

R=(3/5)*x (III)

Using III in I

(3/5)*x+M=x

M=x-(3/5)*x

M=(2/5)*x (IV)

Mikhail filo dough (MF)

Mikhail shortcrust dough (MS)

Rashid filo dough (RF)

Rashid shortcrust dough (RS)

Mikhail used filo dough for all of his pastries

MF=M

MS=0

Rashid used shortcrust dough for all of his pastries

RS=R

RF=0

Filo dough (FD)

FD=RF+MF=0+MF=MF=M (V)

5/8 of the filo dough pastries were brushed with olive oil

pastries brushed with olive oil (OI)

(5/8)*FD=OI

Using V

(5/8)*M=OI

Using IV

(5/8)*(2/5)*x=OI

(1/4)*x=OI (VI)

pastries brushed with butter (B)

Pastries made out of filo dough are brushed with either olive oil or butter (but not both)

FD=OI+B

B=FD-OI

Using V and VI

B= M - (1/4)*x

Using IV

B = (2/5)*x - (1/4)*x

B= (3/20)*x

3X/20 (option a) of the pastries submitted by Rashid and Mikhail were brushed with butter

correct answers below:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.