Question

THIS IS A SUPER IMPORTANT TEST HELP!!!

Paul plans to spend p dollars for a meal at a restaurant and will leave a 20% tip. Paul writes the following expression to calculate the cost of the meal including the 20% tip:

p+0.20p

Which expressions are equivalent to the one Paul wrote?

Drag and drop each expression to the correct box to identify whether it is equivalent or not equivalent.
Equivalent Not Equivalent

2p+0.20 0.80p p(1+0.20) 1.20p 2.20p 1.02p

Answer 1

1. Equivalent:
`p(1+0.20),\ 1.20p;`

2. Not equivalent:
`2p+0.20,\ 0.80p,\ 2.20p,\ 1.02p.`

Explanation:

Consider the expression
`p+0.20p.`

Use the distributive property

`a\cdot (b+c)=a\cdot b+a\cdot c.`

Then

`p+0.20p=p\cdot 1+p\cdot 0.20=p\cdot (1+0.20)=p(1+0.20).`

Expression
`p(1+0.20)` is equivalent to the expression
`p+0.20p.`

Since
`1+0.20=1.20,` then expression
`p(1+0.20)=1.20p` is equivalent to the expression
`p+0.20p.`

All the rest expressions are not equivalent to the expression
`p+0.20p.`