Question

3. One number is 9 more than twice another number. If the sum of the numbers is 129, find both numbers.

4. Jane scored 17 points higher on her second test
then on her first test. If the sum of the scores on
the two tests is 183 points, find the score of each
test.

1. minhkhang
3. The value of one of the numbers is 89 and the other is 40
4. The score on the first test is 83 and score on the second test is 100

Application of simultaneous equations

From the question, we are to determine the value of the numbers
From the given information,
One number is 9 more than twice another number
Let one of the numbers be x and the other be y
Thus,
x = 2y + 9 ——— (1)
Also,
the sum of the numbers is 129
That is,
x + y = 129 ———- (2)
Solving
Substitute equation (1) into equation(2)
x + y = 129
2y + 9 + y = 129
2y + y = 129 – 9
3y = 120
y = 120/3
y = 40
Substitute the value of y into equation (1)
x = 2y + 9
x = 2(40) + 9
x = 80 + 9
x = 89
Hence, one of the numbers is 89 and the other is 40
From the question, we are to determine the scores on each test
Let the score on the first test = m
and score on the second test = n
Jane scored 17 points higher on her second test than on her first test
n = m + 17 ——– (1)
Also,
the sum of the scores on the two tests is 183 points
n + m = 183
Substitute equation (1) into equation(2)
n + m = 183
m + 17 + m = 183
m + m = 183 – 17
2m = 166
m = 166/2
m = 83
Substitute the value of y into equation (1)
n = m + 17
n = 83 + 17
n = 100
Hence, the score on the first test is 83 and score on the second test is 100