In the spring, 80% of the sheep in a flock of sheep had lambs. of those sheep with lambs, 30% had one lamb, 40% had two lambs and the rest had 3 lambs. a total of 240 lambs were born. how many sheep are in the flock? you must show your working.
To solve this problem, we need to work step by step. Let's break it down into smaller parts:
1. Let's say the total number of sheep in the flock is "x."
2. In the spring, 80% of the sheep had lambs. So, 80% of "x" sheep had lambs. This can be calculated by multiplying 80% by "x" or simply multiplying 0.8 by "x".
Number of sheep with lambs = 0.8x
3. Now, we need to find out how many lambs were born. According to the given information, of the sheep with lambs, 30% had one lamb, 40% had two lambs, and the rest had 3 lambs.
Number of lambs born from sheep with one lamb = 0.3 * (0.8x)
Number of lambs born from sheep with two lambs = 0.4 * (0.8x)
4. The question states that a total of 240 lambs were born, so we can add up the number of lambs born from each category.
Number of lambs born = Number of lambs born from sheep with one lamb + Number of lambs born from sheep with two lambs + Number of lambs born from sheep with three lambs
= 0.3 * (0.8x) + 0.4 * (0.8x) + Number of lambs born from sheep with three lambs
5. We know that the total number of lambs born is 240, so we can set up an equation:
240 = 0.3 * (0.8x) + 0.4 * (0.8x) + Number of lambs born from sheep with three lambs
6. We are given that the rest of the sheep (after considering the ones with one or two lambs) had three lambs. So we can calculate the number of lambs born from sheep with three lambs as follows:
Number of lambs born from sheep with three lambs = (0.8x) - (0.3 * (0.8x)) - (0.4 * (0.8x))
7. Substitute this value back into the equation:
240 = 0.3 * (0.8x) + 0.4 * (0.8x) + [(0.8x) - (0.3 * (0.8x)) - (0.4 * (0.8x))]
8. Simplify the equation:
240 = 0.24x + 0.32x + (0.8x - 0.24x - 0.32x)
9. Combine like terms on both sides:
240 = 1.12x + (0.24x - 0.24x - 0.32x)
240 = 1.12x
10. Now, isolate "x" by dividing both sides of the equation by 1.12:
x = 240 / 1.12
x ≈ 214.29
The approximate number of sheep in the flock is around 214.
If you post a problem, remember you are asking for help. I get put off when you say, "you must show your working," first because I do not in fact have to do it at all, and second, it's bad English.
So, rather than just doing a copy and paste, edit it so it looks like you're requesting assistance.
So, on to the problem:
240 lambs were born
80% of sheep had lambs, so there were 240/.8 = 300 sheep in the flock
That answers the question.
If you are interested in how many had 1,2,3 lambs, then
30% of 240 = 72 had 1 lamb
40% of 240 = 96 had 2 lambs
That leaves 30% = 72 had 3 lambs