Math / Algebra

Question1. A student will buy packs of AA batteries, packs of AAA batteries, and 1 pack of $C$ batteries. - The student will buy the same number of packs of AA and AAA batteries. - Each pack of AA batteries costs \ $10. - Each pack of AAA batteries costs \$5. - The pack of$ \mathbf{C} $batteries costs$ \ $18$ . - The student will spend a total of $\$ 108$ .
Which equations can be used to determine $x$ , the number of packs of each of AA batteries and AAA batteries the student will buy? Select all that apply. A. $15 x=90$ B. $23 x=98$ C. $33 x=108$ D. $10+(5+18) x=108$ E. $(10+5) x+18=108$ F. $\quad(10+5+18) x=108$

Studdy Solution

STEP 1

1. Let $x$ be the number of packs of AA batteries.
2. The student buys the same number of packs of AA and AAA batteries.
3. Each pack of AA batteries costs \$10.
4. Each pack of AAA batteries costs \$5.
5. The pack of $ C $ batteries costs \$18.
6. The total amount spent is \$108.

STEP 2

1. Define the expressions for the cost of AA and AAA batteries.
2. Define the expression for the total cost.
3. Set up equations based on the total cost.
4. Identify which equations match the problem conditions.

STEP 3

The cost for $x$ packs of AA batteries is $10x$ .
The cost for $x$ packs of AAA batteries is $5x$ .

STEP 4

The total cost for the AA and AAA batteries is $10x + 5x = 15x$ .
The total cost including the pack of $C$ batteries is $15x + 18$ .

STEP 5

Set up the equation for the total cost:
$15x + 18 = 108$

STEP 6

Simplify the equation to solve for $x$ :
$15x = 108 - 18$
$15x = 90$
This matches option A: $15x = 90$ .

STEP 7

Evaluate other options:
Option E: $(10 + 5)x + 18 = 108$ simplifies to $15x + 18 = 108$ , which is correct.
Option D: $10 + (5 + 18)x = 108$ simplifies to $10 + 23x = 108$ , which is incorrect.
Option F: $(10 + 5 + 18)x = 108$ simplifies to $33x = 108$ , which is incorrect.
The correct equations are:
- Option A: $15x = 90$ - Option E: $(10 + 5)x + 18 = 108$

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Studdy Solution

STEP 1

1. Let $x$ be the number of packs of AA batteries.
2. The student buys the same number of packs of AA and AAA batteries.
3. Each pack of AA batteries costs \$10.
4. Each pack of AAA batteries costs \$5.
5. The pack of \( C \) batteries costs \$18.
6. The total amount spent is \$108.

STEP 2

1. Define the expressions for the cost of AA and AAA batteries.
2. Define the expression for the total cost.
3. Set up equations based on the total cost.
4. Identify which equations match the problem conditions.

STEP 3

The cost for $x$ packs of AA batteries is $10x$ .
The cost for $x$ packs of AAA batteries is $5x$ .

STEP 4

The total cost for the AA and AAA batteries is $10x + 5x = 15x$ .
The total cost including the pack of $C$ batteries is $15x + 18$ .

STEP 5

Set up the equation for the total cost:
$15x + 18 = 108$

STEP 6

Simplify the equation to solve for $x$ :
$15x = 108 - 18$
$15x = 90$
This matches option A: $15x = 90$ .

STEP 7

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Studdy Solution

STEP 1

1. Let x x x be the number of packs of AA batteries.2. The student buys the same number of packs of AA and AAA batteries.3. Each pack of AA batteries costs \$10.4. Each pack of AAA batteries costs \$5.5. The pack of \( C \) batteries costs \$18.6. The total amount spent is \$108.

STEP 2

1. Define the expressions for the cost of AA and AAA batteries.2. Define the expression for the total cost.3. Set up equations based on the total cost.4. Identify which equations match the problem conditions.

STEP 3

The cost for x x x packs of AA batteries is 10x 10x 10x.The cost for x x x packs of AAA batteries is 5x 5x 5x.

STEP 4

The total cost for the AA and AAA batteries is 10x+5x=15x 10x + 5x = 15x 10x+5x=15x.The total cost including the pack of C C C batteries is 15x+18 15x + 18 15x+18.

STEP 5

Set up the equation for the total cost:15x+18=108 15x + 18 = 108 15x+18=108

STEP 6

Simplify the equation to solve for x x x:15x=108−18 15x = 108 - 18 15x=108−1815x=90 15x = 90 15x=90This matches option A: 15x=90 15x = 90 15x=90.

STEP 7

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1. Let $x$ be the number of packs of AA batteries.
2. The student buys the same number of packs of AA and AAA batteries.
3. Each pack of AA batteries costs \$10.
4. Each pack of AAA batteries costs \$5.
5. The pack of \( C \) batteries costs \$18.
6. The total amount spent is \$108.

1. Define the expressions for the cost of AA and AAA batteries.
2. Define the expression for the total cost.
3. Set up equations based on the total cost.
4. Identify which equations match the problem conditions.

The cost for $x$ packs of AA batteries is $10x$ .
The cost for $x$ packs of AAA batteries is $5x$ .

The total cost for the AA and AAA batteries is $10x + 5x = 15x$ .
The total cost including the pack of $C$ batteries is $15x + 18$ .

Set up the equation for the total cost:
$15x + 18 = 108$

Simplify the equation to solve for $x$ :
$15x = 108 - 18$
$15x = 90$
This matches option A: $15x = 90$ .