Answer:
Part 9) The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13
Part 10) The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot
Step-by-step explanation:
Part 9)
Let
x ----> number of items on Emily's grocery list
x ----> number of items on Bobby's grocery list
we know that
[tex]y=2x+3[/tex] ----> equation A
[tex]x=y-8[/tex] ----> equation B
Solve by substitution
Substitute equation A in equation B
[tex]x=(2x+3)-8[/tex]
solve for x
[tex]x=2x-5[/tex]
[tex]2x-x=5[/tex]
[tex]x=5[/tex]
Find the value of y
[tex]y=2(5)+3=13[/tex]
therefore
The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13
Part 10)
Let
x ----> the height of the taller bookshelf in feet
y ----> the height of the shorter bookshelf in feet
we have
[tex]x=5y-1[/tex] ----> equation A
Remember that
[tex]1\ ft=12\ in[/tex]
To convert inches to feet divide by 12
so
[tex]60\ in=60/12=5\ ft[/tex]
[tex]x+y=5[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex](5y-1)+y=5[/tex]
solve for y
[tex]5y+y=5+1[/tex]
[tex]6y=6[/tex]
[tex]y=1\ ft[/tex]
Find the value of x
[tex]x=5(1)-1=4\ ft[/tex]
therefore
The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot
