log(x–4)+log(x+3)=2logx
10,503,970
10,503,097
1,503,097
10,053,097
-3x-2y=-12 by substitution
Answer: x = 0.25, y = 5.625 or (, )
Step-by-step explanation:
To solve by substitution, we will first isolate one of the variables in one of the given equations.
-7x - 2y = -13 ➜ y = -3.5x + 6.5
Then, we will substitute this into the other given equation and solve for x.
-3x - 2y = -12
-3x - 2(-3.5x + 6.5) = -12
-3x + 7x - 13 = -12
4x = 1
x = 0.25
Lastly, we will substitute this value of x into the equation we solved for to find y.
y = -3.5x + 6.5
y = -3.5(0.25) + 6.5
y = 5.625
Answer:
The possible ages of the four grandchildren are a = 4, b = 19, c = 26, and d = 34
Step-by-step explanation:
The given parameters are;
The number of grandchildren in the family = 4
The product of the ages of the four grand children = 67184
The age of the youngest grandchild < 10
The age of the oldest grandchild = 30 + The age of the youngest grandchild
Let a represent the age of the youngest grandchild, and let b, and c represent the ages of the other two intermediate grandchild
Therefore, we have;
a < 10
The age of the oldest grandchild = a + 30 < 10 + 30
∴ The age of the oldest grandchild < 40
The product of the ages of the four grandchildren = a × b × c × (a + 30) = 67184
The factors of 67184 that are between 1 and 40 are;
1, 2, 4, 8, 13, 16, 17, 19, 26, 34, 38
Taking a = 8, we have;
The age of the oldest grandchild × The age of the youngest grandchild = a × (a + 30) = 8 × 38 = 342
Therefore. a × b = 67184/(a × (a + 30) = 196.44
Therefore, a ≠ 8
For a = 4, we have the age of the oldest grandchild = a + 30 = 4 + 30 = 34
The age of the oldest grandchild × The age of the youngest grandchild = a × (a + 30) = 4 × 34 = 136
Therefore. a × b = 67184/(a × (a + 30) = 494
We find that the other factors of 67184, which are 19 and 26 have a product of 494
Therefore, the possible ages of the four grandchildren are a = 4, b = 19, c = 26, and d = 34
To give, 4 × 19 × 26 × 34 = 67,184.