Question

(8)

Amelia wanted to redeem a voucher. She had only 3/5of the total number
of points needed. After she earned another 50 points, she still needed 3/10
of the total number of points. How many points were needed to
redeem the voucher?

Answer 1

To solve this problem, set up an equation using the given information and solve for 'x.' However, the given information in this question equations to a negative value, which is not a valid solution.

Step-by-step explanation:

To solve this problem, we can set up an equation using the given information.

Let's denote the total number of points needed to redeem the voucher as 'x.'

Since Amelia had only 3/5 of the total number of points needed initially, she had (3/5)x points.

After earning another 50 points, she still needed 3/10 of the total number of points, which is (3/10)x points.

From this, we can create the equation (3/5)x + 50 = (3/10)x.

To solve for 'x,' we need to isolate the variable on one side of the equation.

Multiplying both sides of the equation by 10, we get 6x + 500 = 3x.

Subtracting 3x from both sides, we obtain 3x + 500 = 0. Next, subtract 500 from both sides of the equation to get 3x = -500.

Finally, divide both sides by 3 to find that x = -166.7.

Since the number of points needed cannot be negative, the negative value is not valid.

Therefore, there must have been an error in the problem or the given information.

Answer 2

The number of points needed to redeem the voucher is 92.5

Step-by-step explanation:

Let x be the total number of points needed to redeem the voucher.

Amelia has
`(3)/(5)` × x points,before she earns the another 50 points,

After she earns another 50 points,

Now

she has
`(3)/(5)` × x + 50 points.

she still needs
`(3)/(10)` × x points to redeem the voucher.

Now

From above we get a equation,

`(3)/(5)` × x + 50 =
`(9)/(10)` × x

Solving the equation we can get x,

`(3)/(5)` × x =
`(9)/(10)` × x - 50

if we multiply both sides by 5/3, we get,

x = (9/10 × x - 50) × 5/3

After expanding the right side,

x = (9/10 × x - 50) × 5/3

x = (9x/10 - 250/3)

Now,

Subtracting 9x/10 from both sides,

0 = 250/3 - 9x/10

If we add 9x/10 to both sides,

9x/10 = 250/3

Again,

If we multiply both sides by 10/9,

x = 250/3× 10/9

x = 250 × 10 / (3 × 9)

x = 250 × 10 / 27

x = 250 × 10 / 27

x = 250 × 10 / 27

x = 250 × 10 / 27

= 250 × .37

x = 92.5

The number of points needed to redeem the voucher is 92.5