Question

#9 and #10
Please show work

Answer 1

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

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

`y=2x+3` ----> equation A

`x=y-8` ----> equation B

Solve by substitution

Substitute equation A in equation B

`x=(2x+3)-8`

solve for x

`x=2x-5`

`2x-x=5`

`x=5`

Find the value of y

`y=2(5)+3=13`

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

`x=5y-1` ----> equation A

Remember that

`1\ ft=12\ in`

To convert inches to feet divide by 12

so

`60\ in=60/12=5\ ft`

`x+y=5` ----> equation B

Solve the system by substitution

substitute equation A in equation B

`(5y-1)+y=5`

solve for y

`5y+y=5+1`

`6y=6`

`y=1\ ft`

Find the value of x

`x=5(1)-1=4\ ft`

therefore

The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot