Raj's catering company is serving an event for 353535 guests. Each guest will choose either a salad or a bowl of soup. 1. Write an equation that represents how many total salads Raj needs to prepare (sss) when bbb guests choose a bowl of soup.

 Raj's catering company is serving an event for 

$35$35 guests. Each guest will choose either a salad or a bowl of soup.

1. Write an equation that represents how many total salads Raj needs to prepare ($s$s) when $b$b guests choose a bowl of soup.

s=35−b

2. How many salads does Raj need to prepare if $21$21 guests choose a bowl of soup?

 salads

Hint #11 / 4

Strategy

Since each guest chooses either a salad or a bowl of soup, we know that:

$\blueE{\left(\overset{\#\text{ of}}{ \text{salads}}\right)}+\maroonD{\left(\overset{\#\text{ of}}{ \text{bowls of soup}}\right)}=\goldE{\left(\overset{\#\text{ of}}{ \text{guests}}\right)}$start color #0c7f99, left parenthesis, start text, s, a, l, a, d, s, end text, start superscript, \#, start text, space, o, f, end text, end superscript, right parenthesis, end color #0c7f99, plus, start color #ca337c, left parenthesis, start text, b, o, w, l, s, space, o, f, space, s, o, u, p, end text, start superscript, \#, start text, space, o, f, end text, end superscript, right parenthesis, end color #ca337c, equals, start color #a75a05, left parenthesis, start text, g, u, e, s, t, s, end text, start superscript, \#, start text, space, o, f, end text, end superscript, right parenthesis, end color #a75a05

We also know that there are $35$35 guests. Let's use this to write a general equation and to find how many salads Raj needs if $21$21 guests choose a bowl of soup.

Hint #22 / 4

Writing an equation

Since there are $35$35 guests, we know:

$\begin{aligned} \blueE{\left(\overset{\#\text{ of}}{ \text{salads}}\right)}+\maroonD{\left(\overset{\#\text{ of}}{ \text{bowls of soup}}\right)}&=\goldE{\left(\overset{\#\text{ of}}{ \text{guests}}\right)} \\\\ \blueE{s} + \maroonD{b} &= \goldE{35} \end{aligned}$

Let's rewrite this equation so $\blueE{s}$start color #0c7f99, s, end color #0c7f99 is by itself:

$\begin{aligned} s + b &= 35 \\\\ s + b - b &= 35 - b \\\\ s &= 35 - b \end{aligned}$

Hint #33 / 4

How many salads if $21$21 bowls of soups?

Let's use our equation to find the value of $s$s when $b=\maroonD{21}$b, equals, start color #ca337c, 21, end color #ca337c:

$\begin{aligned} s &= 35 - b \\\\ &=35-\maroonD{21} \\\\ &=14 \end{aligned}$

Hint #44 / 4

Answers

If each of $35$35 guests will choose either a salad or a bowl of soup...

1. Our equation is $\boxed{s=35-b}$start box, s, equals, 35, minus, b, end box.

2. Raj needs to prepare $\boxed{14}$start box, 14, end box salads if $21$21 guests choose a bowl of soup.