Lily and Julian start with the same number.

Lily works out half of the number, and Julian works out three-quarters of the number.

The sum of their answers is 275.

What was the starting number? Explain, please.

x - the starting number
2 x ​ + 3 x ​ = 275∣ ⋅ 6 3 x + 2 x = 1650 5 x = 1650 x = 330

Answered by konrad509 | 2024-06-10

The way to solve this problem is by setting up an equation using the information given. If Lily works out half of the number and Julian works out three quarters of the same number, and we know that the sum of their answers is 275, we can express this relationship algebraically.
Let the starting number be x. Then, Lily's answer is 1/2 of x and Julian's answer is 3/4 of x.
Lily's part: 1/2 * x
Julian's part: 3/4 * x
The sum of both parts equals 275:
(1/2 * x) + (3/4 * x) = 275
To find x, we need to solve for it. First, we combine like terms by getting a common denominator:
(2/4 * x) + (3/4 * x) = 275
(2/4 + 3/4) * x = 275
(5/4) * x = 275
Multiply both sides by the reciprocal of 5/4 to get x by itself:
x = 275 * (4/5)
x = 220
Therefore, the starting number was 220.

Answered by EzraMatthewMiller | 2024-06-24

The starting number is 220. This was found by setting up an equation based on the fractions that Lily and Julian calculated from the starting number. After some algebra, we determined the value of the starting number to be 220.
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Answered by konrad509 | 2024-12-26