Math / Algebra

QuestionProblem their of designer sneakers was purchased for $\$ 120$ . Since they were purchased, heir price has increased by $15 \%$ . What is the new price?
2. Elena's aunt bought her a $\$ 150$ savings bond when she was born. When Elena is 20 years old, the bond will have earned $105 \%$ in interest. How much will the bond be worth when Elena is 20 years old?
3. In a video game, Clare scored $50 \%$ more points than Tyler. If $c$ is the number of points that Clare scored and $t$ is the number of points that Tyler scored, which equations are correct? Select all that apply. A. $\quad c=1.5 t$ B. $c=t+0.5$ C. $c=t+0.5 t$ D. $c=t+50$ E. $\quad c=(1+0.5) t$
4. from Unit 4, Lesson 6
Draw a diagram to represent each situation: a. The number of miles driven this month was a $30 \%$ decrease of the number of miles driven last month.

Studdy Solution

STEP 1

What is this asking? We've got a bunch of percentage problems here, dealing with increases, decreases, and even writing equations about them! Watch out! Don't mix up percentages with actual amounts.
A 15% increase isn't the same as adding $\$15$ !
Also, be careful when translating percentage word problems into equations.

STEP 2

1. Sneaker Price Increase
2. Savings Bond Value
3. Video Game Points Equation
4. Miles Driven Diagram

STEP 3

Alright, so the original price of the sneakers is $\$120$ .
They increased in price by 15%.

STEP 4

To find the increase amount, we multiply the original price by the percentage increase (remember to write the percentage as a decimal!): $\$120 \cdot 0.15 = \$18$ .
This means the price went up by $\$18$ !

STEP 5

Now, to find the new price, we add the increase to the original price: $\$120 + \$18 = \$138$ .
So, the new price of the sneakers is $\$138$ !

STEP 6

Elena's savings bond started at $\$150$ .
It earned 105% interest.

STEP 7

Let's calculate the interest earned: $\$150 \cdot 1.05 = \$157.50$ .
That's how much the bond earned in interest over the years.

STEP 8

The final value of the bond is the original amount plus the interest: $\$150 + \$157.50 = \$307.50$ .
So, when Elena turns 20, the bond will be worth $\$307.50$ !

STEP 9

Clare scored 50% more points than Tyler.
Let's represent Clare's score with $c$ and Tyler's score with $t$ .

STEP 10

"50% more than Tyler" means Tyler's score ( $t$ ) plus 50% of Tyler's score ( $0.5t$ ).
So, $c = t + 0.5t$ .
This matches option C!

STEP 11

We can simplify $t + 0.5t$ to $1.5t$ , so $c = 1.5t$ .
This matches option A!

STEP 12

Also, we can rewrite $1.5t$ as $(1 + 0.5)t$ , which matches option E!
Options B and D are incorrect because adding 0.5 or 50 doesn't represent a 50% increase.

STEP 13

This month's miles are a 30% decrease from last month's miles.

STEP 14

Let's draw a bar.
The full bar represents last month's miles.

STEP 15

Now, let's divide the bar into 10 equal sections.
Each section represents 10%.

STEP 16

A 30% decrease means we shade 3 of those sections.
The remaining unshaded 7 sections (70%) represent this month's miles.

STEP 17

1. The new price of the sneakers is $\$138$ .
2. The bond will be worth $\$307.50$ when Elena is 20.
3. The correct equations are A ( $c = 1.5t$ ), C ( $c = t + 0.5t$ ), and E ( $c = (1 + 0.5)t$ ).
4. The diagram shows a bar divided into 10 sections, with 3 sections shaded to represent the 30% decrease, leaving 7 sections for this month's miles.

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Studdy Solution

STEP 1

STEP 2

1. Sneaker Price Increase
2. Savings Bond Value
3. Video Game Points Equation
4. Miles Driven Diagram

STEP 3

Alright, so the original price of the sneakers is $\$120$ .
They increased in price by 15%.

STEP 4

To find the increase amount, we multiply the original price by the percentage increase (remember to write the percentage as a decimal!): $\$120 \cdot 0.15 = \$18$ .
This means the price went up by $\$18$ !

STEP 5

Now, to find the new price, we add the increase to the original price: $\$120 + \$18 = \$138$ .
So, the new price of the sneakers is $\$138$ !

STEP 6

Elena's savings bond started at $\$150$ .
It earned 105% interest.

STEP 7

Let's calculate the interest earned: $\$150 \cdot 1.05 = \$157.50$ .
That's how much the bond earned in interest over the years.

STEP 8

The final value of the bond is the original amount plus the interest: $\$150 + \$157.50 = \$307.50$ .
So, when Elena turns 20, the bond will be worth $\$307.50$ !

STEP 9

Clare scored 50% more points than Tyler.
Let's represent Clare's score with $c$ and Tyler's score with $t$ .

STEP 10

"50% more than Tyler" means Tyler's score ( $t$ ) plus 50% of Tyler's score ( $0.5t$ ).
So, $c = t + 0.5t$ .
This matches option C!

STEP 11

We can simplify $t + 0.5t$ to $1.5t$ , so $c = 1.5t$ .
This matches option A!

STEP 12

Also, we can rewrite $1.5t$ as $(1 + 0.5)t$ , which matches option E!
Options B and D are incorrect because adding 0.5 or 50 doesn't represent a 50% increase.

STEP 13

This month's miles are a 30% decrease from last month's miles.

STEP 14

Let's draw a bar.
The full bar represents last month's miles.

STEP 15

Now, let's divide the bar into 10 equal sections.
Each section represents 10%.

STEP 16

A 30% decrease means we shade 3 of those sections.
The remaining unshaded 7 sections (70%) represent this month's miles.

STEP 17

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Studdy Solution

STEP 1

STEP 2

1. Sneaker Price Increase2. Savings Bond Value3. Video Game Points Equation4. Miles Driven Diagram

STEP 3

Alright, so the **original price** of the sneakers is $120\$120$120.They increased in price by **15%**.

STEP 4

To find the **increase amount**, we multiply the original price by the percentage increase (remember to write the percentage as a decimal!): $120⋅0.15=$18\$120 \cdot 0.15 = \$18$120⋅0.15=$18.This means the price went up by $18\$18$18!

STEP 5

Now, to find the **new price**, we add the increase to the original price: $120+$18=$138\$120 + \$18 = \$138$120+$18=$138.So, the new price of the sneakers is $138\$138$138!

STEP 6

Elena's savings bond started at $150\$150$150.It earned **105%** interest.

STEP 7

Let's calculate the **interest earned**: $150⋅1.05=$157.50\$150 \cdot 1.05 = \$157.50$150⋅1.05=$157.50.That's how much the bond earned in interest over the years.

STEP 8

The **final value** of the bond is the original amount plus the interest: $150+$157.50=$307.50\$150 + \$157.50 = \$307.50$150+$157.50=$307.50.So, when Elena turns 20, the bond will be worth $307.50\$307.50$307.50!

STEP 9

Clare scored 50% more points than Tyler.Let's represent Clare's score with ccc and Tyler's score with ttt.

STEP 10

"50% more than Tyler" means Tyler's score (ttt) plus 50% of Tyler's score (0.5t0.5t0.5t).So, c=t+0.5tc = t + 0.5tc=t+0.5t.This matches option C!

STEP 11

We can simplify t+0.5tt + 0.5tt+0.5t to 1.5t1.5t1.5t, so c=1.5tc = 1.5tc=1.5t.This matches option A!

STEP 12

Also, we can rewrite 1.5t1.5t1.5t as (1+0.5)t(1 + 0.5)t(1+0.5)t, which matches option E!Options B and D are incorrect because adding 0.5 or 50 doesn't represent a 50% increase.

STEP 13

This month's miles are a 30% decrease from last month's miles.

STEP 14

Let's draw a bar.The full bar represents last month's miles.

STEP 15

Now, let's divide the bar into 10 equal sections.Each section represents 10%.

STEP 16

A 30% decrease means we shade 3 of those sections.The remaining unshaded 7 sections (70%) represent this month's miles.

STEP 17

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1. Sneaker Price Increase
2. Savings Bond Value
3. Video Game Points Equation
4. Miles Driven Diagram

Alright, so the original price of the sneakers is $\$120$ .
They increased in price by 15%.

To find the increase amount, we multiply the original price by the percentage increase (remember to write the percentage as a decimal!): $\$120 \cdot 0.15 = \$18$ .
This means the price went up by $\$18$ !

Now, to find the new price, we add the increase to the original price: $\$120 + \$18 = \$138$ .
So, the new price of the sneakers is $\$138$ !

Elena's savings bond started at $\$150$ .
It earned 105% interest.

Let's calculate the interest earned: $\$150 \cdot 1.05 = \$157.50$ .
That's how much the bond earned in interest over the years.

The final value of the bond is the original amount plus the interest: $\$150 + \$157.50 = \$307.50$ .
So, when Elena turns 20, the bond will be worth $\$307.50$ !

Clare scored 50% more points than Tyler.
Let's represent Clare's score with $c$ and Tyler's score with $t$ .

"50% more than Tyler" means Tyler's score ( $t$ ) plus 50% of Tyler's score ( $0.5t$ ).
So, $c = t + 0.5t$ .
This matches option C!

We can simplify $t + 0.5t$ to $1.5t$ , so $c = 1.5t$ .
This matches option A!

Also, we can rewrite $1.5t$ as $(1 + 0.5)t$ , which matches option E!
Options B and D are incorrect because adding 0.5 or 50 doesn't represent a 50% increase.

Let's draw a bar.
The full bar represents last month's miles.

Now, let's divide the bar into 10 equal sections.
Each section represents 10%.

A 30% decrease means we shade 3 of those sections.
The remaining unshaded 7 sections (70%) represent this month's miles.