Question

Ryan is 4 1/2 ft. tall. He is 3 in. taller than his sister Lizzie. She is 3/4 of a foot taller than her sister Emma. How tall is Emma ?

Answer 1

Answer:

$3\frac{1}{12}$ ft tall

Step-by-step explanation:

We must follow the indications:

Ryan is 4 1/2 ft. tall.

Ryan = $4\frac{1}{12} ft$

He is 3 in. taller than his sister Lizzie. to find how tall is Lizzie we need to substract 3 inches from the height of Ryan, but we can only substract the quantities if they are in the same units.

Thus we convert the 3 inches to feet, since we 1 feet = 12 inches:

$\frac{1}{4} feet=3inches$

so the height of lizzie:

$4\frac{1}{12}ft-\frac{1}{4}ft$

we convert the first mixed number to fraction by multiplying 4 by 12 and adding the numerator 1:

$4\frac{1}{12}=\frac{4*12+1}{12}=\frac{49}{12}$

the subtraction becomes:

$\frac{49}{12}ft-\frac{1}{4}ft\\ \\=\frac{49*4-12*1}{12*4}\\ \\=\frac{196-12}{48}\\\\=\frac{184}{48}\\ \\=\frac{46}{12}$

$=\frac{23}{6}$

Lizzie is 23/6 ft tall.

She is 3/4 of a foot taller than her sister Emma, thus we must substract 3/4 from the height of Lizzie to find the height of Emma:

$\frac{23}{6}ft-\frac{3}{4}ft\\ \\=\frac{23*4-6*3}{6*4}\\ \\=\frac{92-18}{24}\\ \\=\frac{74}{24}\\ \\=\frac{37}{12}\\ \\=3\frac{1}{12}$

Emma is $3\frac{1}{12}$ ft tall.