the weight of 4 boxes together is 66.5kg.the weight of box B is 2kg less than box A.and the weight of box C is 1.5kg more than box A.if the weight of box D is 1.5kg more than box C.find the weight of each box
look at what we have:
a+b+c+d = 66.5
b = a-2
c = a+1.5
d = c+1.5
Start substituting:
a+(a-2)+(a+1.5)+((a+1.5)+1.5) = 66.5
a=16.0
b=14.0
c=17.5
d=19.0
b = a-2
c = a+1.5
d = c+1.5 = a+1.5 + 1.5 = a+3
a+b+c+d = 66.5
a + a-2 + a+1.5 + a+3 = 66.5
4a = 64
a= 16
box A = 16
box B = 14
box C = 17.5
box D = 19
check:
sum = 66.5
All is good.
Is it correct
To find the weight of each box, we can use algebraic equations based on the given information.
Let's assume that the weight of box A is x kg.
Given that:
- The weight of box B is 2 kg less than box A, so the weight of box B is (x - 2) kg.
- The weight of box C is 1.5 kg more than box A, so the weight of box C is (x + 1.5) kg.
- The weight of box D is 1.5 kg more than box C, so the weight of box D is ((x + 1.5) + 1.5) kg.
According to the problem, the weight of 4 boxes together is 66.5 kg. Therefore, we can write the equation as:
x + (x - 2) + (x + 1.5) + ((x + 1.5) + 1.5) = 66.5
Now we can solve this equation to find the weight of each box:
4x + 3 = 66.5
4x = 66.5 - 3
4x = 63.5
x = 63.5/4
x ≈ 15.875
Therefore, the weight of box A is approximately 15.875 kg, the weight of box B is approximately (15.875 - 2) kg ≈ 13.875 kg, the weight of box C is approximately (15.875 + 1.5) kg ≈ 17.375 kg, and the weight of box D is approximately ((17.375 + 1.5) + 1.5) kg ≈ 20.375 kg.