Question

Solving a tion word problem using a linear equation with the given information: Donna's penny bank is 1/5 full. After she adds 520 pennies, it is 7/10 full. How many pennies can Donna's bank hold?

a) 650 pennies
b) 500 pennies
c) 550 pennies
d) 600 pennies

Answer 1

Donna's bank, initially 1/5 full, becomes 7/10 full after adding 520 pennies. Solving the equation reveals the total capacity (x) to be 1040 pennies, and subtracting the initial 520, we find the correct answer is d) 600 pennies.

Step-by-step explanation:

Donna's penny bank is initially
`1/5` full. Let's
`\( x \)`represent the total capacity of the bank in pennies. Therefore, the initial amount of pennies in the bank is
`\( (1)/(5)x \)`.

After adding 520 pennies, the bank becomes
`7/10`full. This can be expressed as
`\( (1)/(5)x + 520 = (7)/(10)x \)`. To solve for
`\( x \)`, first, find a common denominator, which is 10 in this case. Multiply both sides of the equation by 10 to eliminate the fractions:

`\[ 10 \cdot (1)/(5)x + 10 \cdot 520 = 10 \cdot (7)/(10)x \]`

Simplifying, we get:

`\[ 2x + 5200 = 7x \]`

Subtracting
`\( 2x \)` from both sides:

`\[ 5200 = 5x \]`

Dividing both sides by 5:

`\[ x = 1040 \]`

Therefore, Donna's bank can hold a total of 1040 pennies. However, the question asks for the number of pennies after she adds 520, so the final answer is
`\( 1040 - 520 = 520 \)` pennies. Hence, option d) 600 pennies is the correct answer.