Solve Worded Simultaneous Equations: Tips & Examples

In summary, the conversation is about seeking guidance on solving worded simultaneous questions for exams. The problem presented involves buying bolts and nails for a total of \$112, with bolts costing \$2 and nails costing \$1 and a ratio of 3 bolts to 1 nail. An equation can be set up to solve for the number of bolts and nails purchased.
  • #1
mclarey
1
0
Hello, I am going over past exam questions in preparation for exams and I am horrible at worded questions, can someone please give me some guidance in working out this equation? Or in general how to figure out how to solve worded simultaneous questions? Many thanks :)

You have spent \$112 on nails and bolts. Bolts cost \$2 and nails cost \$1. You bought 3
times as many bolts as nails. How many of each did you buy?
 
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  • #2
Hello and welcome to MHB! (Wave)

I would first let $B$ be the number of bolts purchased and $N$ be the number of nails.

We know the amount spent on bolts plus the amount spent on nails totals 112 dollars. The number of bolts times the cost per bolt is the amount spent on bolts, and likewise the number of nails times the cost per nail is the amount spend on nails. Can you put this together to obtain an equation?
 

Related to Solve Worded Simultaneous Equations: Tips & Examples

What are simultaneous equations?

Simultaneous equations are a set of two or more equations that contain multiple variables and can be solved simultaneously to find the values of those variables.

What are worded simultaneous equations?

Worded simultaneous equations are a type of simultaneous equations that are presented in word problems or real-life scenarios. They require the equations to be translated from words into mathematical expressions before they can be solved.

What are some tips for solving worded simultaneous equations?

1. Read the problem carefully and identify the unknown variables.
2. Create equations using the given information in the problem.
3. Solve one equation for one variable and substitute it into the other equation.
4. Solve the resulting equation for the remaining variable.
5. Check your solution by plugging it back into the original equations.

Can you provide an example of solving a worded simultaneous equation?

Example: A farmer has a total of 30 chickens and pigs on his farm. If the total number of legs is 86, how many chickens and pigs does he have?
Step 1: Let c = number of chickens and p = number of pigs.
Step 2: c + p = 30 (equation for total number of animals)
Step 3: 2c + 4p = 86 (equation for total number of legs)
Step 4: Solve for c in the first equation: c = 30 - p
Step 5: Substitute c = 30 - p into the second equation: 2(30 - p) + 4p = 86
Step 6: Simplify and solve for p: 60 - 2p + 4p = 86
2p = 26
p = 13
Step 7: Substitute p = 13 into the first equation to solve for c: c + 13 = 30
c = 17
Therefore, the farmer has 17 chickens and 13 pigs on his farm.

What are some common mistakes to avoid when solving worded simultaneous equations?

1. Misinterpreting the given information in the problem.
2. Not setting up the correct equations for the problem.
3. Not solving for one variable before substituting into the other equation.
4. Making calculation errors when solving the equations.
5. Forgetting to check the solution in the original equations.

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