Hey everybody, I really need help solving these math equations. Thank YOU! For helping me!
Use Systematic trial to find the value of each variable.
a) 5+7c=89 b) 26=5+3e c) 8k-16=200
d)525-6u=339
Write each sentence as an equation. Solve each equation.
a) four times a number plus one-hundred is 140.
b) seven times a number is 294
c) four times a number minus 52 is 212
a.
5+7c=89
try 10
75
try 14
103
try 12
89
a.
4n+100=140
Sure, I'd be happy to help you solve these math equations using systematic trial.
Let's start with the first set of equations:
a) 5 + 7c = 89
To solve for c, we need to isolate the variable on one side of the equation. Let's subtract 5 from both sides:
7c = 89 - 5
Simplifying the right side:
7c = 84
To get the value of c, we divide both sides by 7:
c = 12
So, the value of c is 12.
b) 26 = 5 + 3e
To solve for e, we'll follow a similar process. Let's subtract 5 from both sides:
26 - 5 = 3e
21 = 3e
To get the value of e, we divide both sides by 3:
e = 7
So, the value of e is 7.
c) 8k - 16 = 200
To solve for k, let's first add 16 to both sides of the equation:
8k - 16 + 16 = 200 + 16
8k = 216
To isolate k, we divide both sides by 8:
k = 27
So, the value of k is 27.
d) 525 - 6u = 339
To solve for u, let's subtract 525 from both sides:
525 - 525 - 6u = 339 - 525
-6u = -186
To isolate u, we divide both sides by -6 (or multiply both sides by -1/6):
u = -186 / -6
Simplifying the division:
u = 31
So, the value of u is 31.
Now, let's move on to the next set of equations:
a) "Four times a number plus one-hundred is 140"
To write this as an equation, we first need to assign a variable to the unknown number. Let's call it x.
So, "four times a number" can be written as 4x. And "plus one-hundred" is +100. The equation becomes:
4x + 100 = 140
To solve for x, let's subtract 100 from both sides:
4x + 100 - 100 = 140 - 100
4x = 40
To isolate x, divide both sides by 4:
x = 40 / 4
Simplifying the division:
x = 10
So, the unknown number is 10.
b) "Seven times a number is 294"
Let's assign the variable y to the unknown number. "Seven times a number" can be written as 7y. The equation becomes:
7y = 294
To solve for y, we divide both sides by 7:
7y / 7 = 294 / 7
y = 42
So, the unknown number is 42.
c) "Four times a number minus 52 is 212"
Let's assign the variable z to the unknown number. "Four times a number" is 4z. "Minus 52" is -52. The equation becomes:
4z - 52 = 212
To solve for z, let's add 52 to both sides:
4z - 52 + 52 = 212 + 52
4z = 264
To isolate z, divide both sides by 4:
z = 264 / 4
Simplifying the division:
z = 66
So, the unknown number is 66.