Sara got 85% and 89% on her first two Maths tests. What must she get
on her third test to have at least a 90% test average.
Assume three tests, represent the problem with an inequality and
then solve it.
Add up all the points. You need x where
85+89+x >= 3*90
96
To represent the problem with an inequality, we can use the average formula:
Average = (sum of scores) / (number of tests)
Let's assume Sara needs to score x% on her third test to have at least a 90% average. We can write the inequality as:
(85 + 89 + x) / 3 ≥ 90
Now, let's solve it step by step:
1. Multiply both sides of the inequality by 3 to get rid of the fraction:
85 + 89 + x ≥ 270
2. Combine like terms:
174 + x ≥ 270
3. Subtract 174 from both sides of the inequality:
x ≥ 270 - 174
x ≥ 96
Therefore, Sara must score 96% or higher on her third test to have at least a 90% test average.
To represent the problem with an inequality, we can use the average formula. The average is equal to the sum of all the values divided by the number of values. In this case, we have three tests, so the average (A) can be represented as:
A = (85 + 89 + x) / 3,
where x is the score on the third test that we want to find.
We want the average to be at least 90%, so the inequality can be written as:
A ≥ 90.
Substituting the average formula into the inequality, we have:
(85 + 89 + x) / 3 ≥ 90.
To solve this inequality, let's simplify it:
(174 + x) / 3 ≥ 90.
Now, let's solve for x by multiplying both sides of the inequality by 3:
174 + x ≥ 270.
Next, subtract 174 from both sides of the inequality:
x ≥ 270 - 174.
Simplifying further, we have:
x ≥ 96.
Therefore, Sara must score at least 96 on her third math test to have at least a 90% test average.