Answer:
Sally is 42 in. tall, and Jack is 48 in. tall.
Step-by-step explanation:
There are some words missing in the problem.
Perhaps the problem was meant to read:
"The ratio of Sally's height to Jack's height is 7:8. If the sum of their heights is 90 inches, how tall are Sally and Jack?"
Solution:
The ratio of the heights is 7:8.
Sally could measure 7 inches and Jack 8 inches, but then when you add the heights, 7 in. + 8 in. = 15 in. which is not 90 inches.
If you multiply both numbers in a ratio by the same number, the new numbers are still in the same ratio.
Multiply 7 and 8 by 2. You get 14 and 16. Maybe Sally is 14 in. tall and Jack is 16 in. tall. Add the heights, 14 in. + 16 in. = 30 in. This is also not 90 in.
We can keep on guessing what number to multiply by 7 and 8 by so their sum is 90, but we can use algebra to write an equation and not have to go through many guesses.
There is a number, x, that when you multiply 7 and 8 by x, the sum of the products is 90. We don't know what x is, but we can write an equation and solve for x.
The numbers in the ratio are 7x and 8x.
7x and 8x are still in the ratio 7:8.
Now we add the numbers 7x and 8x and set the sum equal to 90. Then we solve for x.
7x + 8x = 90
15x = 90
x = 6
We get x = 6. Now we know we need to multiply both 7 and 8 by 6 to get the heights we need.
7 in. * 6 = 42 in.
8 in. * 6 = 48 in.
Check: 42 in. + 48 in. = 90 in.
Answer: Sally is 42 in. tall, and Jack is 48 in. tall.
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