MHB Solve Worded Simultaneous Equations: Tips & Examples

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To solve the worded simultaneous equations, define variables for the quantities involved, such as B for bolts and N for nails. The total cost equation can be expressed as 2B + N = 112, reflecting the costs of bolts and nails. Additionally, since there are three times as many bolts as nails, the relationship can be represented as B = 3N. By substituting this relationship into the cost equation, you can solve for the number of nails and bolts. Understanding how to translate word problems into equations is key to mastering similar questions.
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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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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?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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