Question

How do I solve these?1) Evaluate the expression, 2b+(c-3a) when a= -1/2, b= 3/4, c= 1/4.2) A store manager uses a markup rate of 24% on all appliances. Find the cost of a coffee maker that sells for $77.50. Use formula S=C+r•C, where S is the selling price, C is the cost, and r is the markup rate.

Answer 1

To evaluate the expression

`2b+(c-3a)`

Plug in the corresponding values that are given and operate, as following:

`\begin{gathered} 2b+(c-3a) \\ \\ \rightarrow2((3)/(4))+((1)/(4)-3(-(1)/(2))) \\ \\ \rightarrow(3)/(2)+((1)/(4)+(3)/(2)) \\ \\ \rightarrow(3)/(2)+(1)/(4)+(3)/(2) \end{gathered}`

At this point, we have to have all our fractions with the same denominator to add them up. To do so, let's find the LCM (Least Common Multiple) between our different denominators (In this case, 2 and 4)

The LCM is 4. Now, we need to find a way for all our fractions to have 4 as a denominator. Notice that we can do so by multiplying both 3/2 by 2 (both in the numerator and denominator), as following:

`\begin{gathered} (3)/(2)+(1)/(4)+(3)/(2)\rightarrow(2\cdot3)/(2\cdot2)+(1)/(4)+(2\cdot3)/(2\cdot2) \\ \\ \rightarrow(6)/(4)+(1)/(4)+(6)/(4) \end{gathered}`

Now, we can add them up:

`(6)/(4)+(1)/(4)+(6)/(4)\rightarrow(6+1+6)/(4)\rightarrow(13)/(4)`

This way, the answer is 13/4