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BartSMP [9]
3 years ago
6

Compare and contrast expanding and simplifying algebraic expressions with simplifying numeric expressions. For example, compare

simplifying 3(x – 2) + (x – 1) with 3(5 – 2) + (5 – 1).
20 POINTS
Mathematics
2 answers:
sammy [17]3 years ago
7 0
Algebraic expressions have terms. Terms must be added to add or subtract and you can't always do order of operations with algebraic expressions.
larisa [96]3 years ago
4 0
<span>With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.</span>
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Answer:

An apple costs $2.25. A mango costs $1.25.

Step-by-step explanation:

Let a = price of 1 apple.

Let m = price of 1 mango.

Cameron:

4 apples + 7 mangoes ----> total $17.75

4a + 7m = 17.75

Gavin:

2 apples + 5 mangoes ----> total $10.75

2a + 5m = 10.75

We have a system of 2 equations in 2 unknowns.

4a + 7m = 17.75

2a + 5m = 10.75

We can use the elimination method to eliminate the variable <em>a</em>. Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Then add the equations.

           4a + 7m = 17.75

(+)       -4a - 10m = -21.5

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                    -3m = -3.75

Divide both sides by -3.

m = 1.25

<em>A mango costs $1.25.</em>

Now we use the first equation and substitute 1.25 for <em>m</em> and solve for <em>a</em>.

4a + 7m = 17.75

4a + 7(1.25) = 17.75

4a + 8.75 = 17.75

4a = 9

a = 2.25

<em>An apple costs $2.25.</em>

Answer: An apple costs $2.25. A mango costs $1.25.

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