Question

Danny works in an amusement park and used a total of 45 strands of lights to decorate 1 bush and 4 trees in the morning. In the afternoon, he used 70 strands to decorate 4 bushes and 5 trees. Assuming all bushes are decorated one way and all trees another, how many strands did Danny use on each?

a) Bushes: 10, Trees: 5
b) Bushes: 8, Trees: 7
c) Bushes: 7, Trees: 8
d) Bushes: 5, Trees: 10

Answer 1

Danny used 5 strands on each bush and 10 strands on each tree.

Step-by-step explanation:

To find out how many strands Danny used on each, we need to set up and solve a system of equations. Let's represent the number of strands used on a bush as 'b' and the number of strands used on a tree as 't'. According to the given information, we have:

1b + 4t = 45 (equation 1)

4b + 5t = 70 (equation 2)

To solve this system, we can use the elimination or substitution method. Let's use the elimination method:

Multiplying equation 1 by 5 and equation 2 by 4, we get:

5b + 20t = 225 (equation 3)

16b + 20t = 280 (equation 4)

Now, subtracting equation 3 from equation 4, we get:

16b + 20t - (5b + 20t) = 280 - 225

11b = 55

b = 5

Substituting the value of b into equation 1, we can find t:

1(5) + 4t = 45

5 + 4t = 45

4t = 40

t = 10

Therefore, Danny used 5 strands on each bush and 10 strands on each tree.