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## Solving Word Problems Using Algebraic Equations

**Example:** Solve the following word problem using algebra

*On Ellie’s trip to the beach she counted 29 different birds! There were a lot of big Seagulls and little Sandpipers but she also saw some Pelicans and even a few Herons. When Ellie got back home she tried to remember all of the different birds she saw so she could tell her family about her school trip. She remembered that she saw 10 seagulls and 7 Sandpipers but she couldn’t remember exactly how many Pelicans and Herons she saw. All she can remember was that she saw twice as many Pelicans as Herons. Based on this information and the bar graph alone help Ellie complete her bar graph. *

Treat this like a word problem but read the words and the bar graph!

Step 1: Underline relevant information:

*On Ellie’s trip to the beach she counted **29 different birds**! There were a lot of big Seagulls and little Sandpipers but she also saw some Pelicans and even a few Herons. When Ellie got back home she tried to remember all of the different birds she saw so she could tell her family about her school trip. She remembered that she saw **10 seagulls** and **7 Sandpipers** but she couldn’t remember exactly how many Pelicans and Herons she saw. All she can remember was that she **saw twice as many Pelicans as Herons**. Based on this information and the bar graph alone help Ellie complete her bar graph. *

Step 2:** **Summarize the information you learned from the bar graph.

Seagulls (SG) = 10

Sandpipers (SP) = 7

Pelicans (P) = ?

Herons (H) = ?

Step 3: Translate the words from the paragraph into mathematical expression. Since we don’t know the number of Pelicans and Herons let’s use a, ‘P’ for Pelican and a ‘H’ for Heron.

Total number of birds equals = 29

SG + SP + P + H = 29

*(equation 1)* 29 = 7 + 10 + P + H *(1)*

29 = 17 + P + H *(2)*

29 – 17 = P + H *(3)*

12 = P + H *(4)*

Let’s go through this step by step

*(1)* Add the numbers on the right-hand side of the equation together, 7 + 10 = 17

*(2)* This leaves us with 29 = 17 + P + H

*(3)* Now we need to isolate the P and H by moving the 17 to the other side of the equation. We can do this by apply the opposite of ‘+17’ which is ‘-17’ to each side

29 – 17 = 17 – 17 P + H > 29 – 17 = P + H

*(4) *Now simply subtract 17 from 29 to complete the equation

12 = P + H

We also know that: Ellie saw twice as many Pelicans as Herons. Another way of saying this is that she saw half as many Herons as Pelicans. Let’s rewrite that using math:

To solve equation 1 we need to get rid of one of the variables. We can do this my substituting in equation 2 to equation 1. Let’s substitute 2 x H in for P.

*(equation 3)* 12 = P + H becomes 12 = (2 x H) + H

Let’s simplify 12 = (2 x H) + H = 2H + H = 3H

Now we have, 12 = 3H

Isolate your H by applying the opposite of times 3 to each side. In other words divide both sides by 3.

12/3 = 3H/3

12 divided by 3 equals 4, 3H divided by 3 equal H since the 3’s cancel.

This leaves us with,

H = 4

Now let’s plug H back into *equation 2 to solve for P :* 2 x H = P

2 x 4 = P

P = 8

Now we can finish our graph!

Let’s check our work by plugging our variables into our original equation

SG + SP + P + H = 29

10 + 7 + 8 + 4 = 29

check!

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Remember how to solve for a variable in an algebraic equation? What about translating a word problem with alegabra? Don’t worry, you’re not alone and Homework Unlocked is here to help. Homework Unlocked offers homework help to parents so you can help your kids excel in math. Here, Homework Unlocked reviews how to translate a word problem into mathematical language using algebra.