Question

example 3

1. rectangles the formula ( p = 2 l + 2 w ) represents the perimeter of a rectangle. in this formula,

( l ) is the length of the rectangle and ( w ) is the width.
a. solve the formula for ( l ).
b. find the length when the width is 4 meters and the perimeter is 36 meters.

1. baseball the formula ( a = \frac { h } { b } ) can be used to find the batting average ( a ) of a batter who has

( h ) hits in ( b ) times at bat.
a. solve the formula for ( b ).
b. if a batter has a batting average of 0.325 and has 39 hits, how many times has the player
been at bat?

1. shopping thomas went to the store to buy videogames for ( $ 13.50 ) each and controllers. the

total amount thomas spent can be represented by ( c = 13.50 g + p ), where ( c ) is the total cost, ( g ) is
the number of games he bought, and ( p ) is the cost of the controllers. the controllers cost ( $ 55 ) and
thomas spent ( $ 136 ) total.
a. solve the equation for ( g ).
b. find how many games thomas bought.

Explanation:

19. RECTANGLES

a. Solve the formula \(P = 2l+2w\) for \(l\)

Step1: Subtract \(2w\) from both sides

\(P - 2w=2l + 2w-2w\)
\(P - 2w = 2l\)

Step2: Divide both sides by \(2\)

\(\frac{P - 2w}{2}=\frac{2l}{2}\)
\(l=\frac{P - 2w}{2}\)

b. Find the length when \(w = 4\) meters and \(P = 36\) meters

Step1: Substitute \(P = 36\) and \(w = 4\) into \(l=\frac{P - 2w}{2}\)

\(l=\frac{36-2\times4}{2}\)

Step2: Simplify the numerator

\(36-2\times4=36 - 8=28\)

Step3: Divide by \(2\)

\(l=\frac{28}{2}=14\)

Step1: Multiply both sides by \(b\)

\(a\times b=\frac{h}{b}\times b\)
\(ab = h\)

Step2: Divide both sides by \(a\)

\(\frac{ab}{a}=\frac{h}{a}\)
\(b=\frac{h}{a}\)

b. Find \(b\) when \(a = 0.325\) and \(h = 39\)

Step1: Substitute \(a = 0.325\) and \(h = 39\) into \(b=\frac{h}{a}\)

\(b=\frac{39}{0.325}\)

Step2: Calculate the division

\(b = 120\)

Step1: Subtract \(p\) from both sides

\(c-p=13.50g + p - p\)
\(c - p=13.50g\)

Step2: Divide both sides by \(13.50\)

\(\frac{c - p}{13.50}=\frac{13.50g}{13.50}\)
\(g=\frac{c - p}{13.50}\)

b. Find \(g\) when \(c = 136\) and \(p = 55\)

Step1: Substitute \(c = 136\) and \(p = 55\) into \(g=\frac{c - p}{13.50}\)

\(g=\frac{136 - 55}{13.50}\)

Step2: Simplify the numerator

\(136-55 = 81\)

Step3: Divide by \(13.50\)

\(g=\frac{81}{13.50}=6\)

Answer:

a. \(l=\frac{P - 2w}{2}\)
b. \(14\) meters

20. BASEBALL

a. Solve the formula \(a=\frac{h}{b}\) for \(b\)