At the market, a pear costs b cents and an apple costs 7 cents less than a pear. Randy buys 4...

Question:

At the market, a pear costs {eq}b {/eq} cents and an apple costs {eq}7 {/eq} cents less than a pear. Randy buys {eq}4 {/eq} pears and an apple. How much does Randy pay in terms of {eq}b {/eq}?

Sentence to Expression:

We can translate a sentence into an expression by using algebraic operations. Here, we use + for "more than", - for "less than, multiplication for "times" etc.

Answer and Explanation:

Let us assume the costs of one pear and one apple be {eq}P {/eq} and {eq}A {/eq} cents respectively.

The problem says, "a pear costs {eq}b {/eq} cents".

So we have:

$$\begin{align} P&=b & \rightarrow (1) \end{align} $$

The problem also says, "an apple costs {eq}7 {/eq} cents less than a pear".

So we get:

$$\begin{align} A&=P-7 \\ A&= b-7 & [ \text{From (1)} ] & \rightarrow (2) \end{align} $$

The problem says, "Randy buys {eq}4 {/eq} pears and an apple".

So the total cost is:

$$\begin{align} 4P + A &= 4b + (b-7) & [ \text{From (1) and (2)} ]\\[0.3cm] &= \color{blue}{\boxed{\mathbf{(5b-7) \text{ cents}}}} & [\because 4b+b=5b] \end{align} $$


Learn more about this topic:

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Solving Word Problems with Algebraic Addition Expressions

from 6th-8th Grade Math: Practice & Review

Chapter 32 / Lesson 8
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