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In the following exercises, translate to a system of equations. Do not solve the system.
The sum of two numbers is fifteen. One number is three less than the other. Find the numbers.
The numbers are 6 and 9.
The sum of two numbers is twenty-five. One number is five less than the other. Find the numbers.
The sum of two numbers is negative thirty. One number is five times the other. Find the numbers.
The numbers are −5 and −25.
The sum of two numbers is negative sixteen. One number is seven times the other. Find the numbers.
Twice a number plus three times a second number is twenty-two. Three times the first number plus four times the second is thirty-one. Find the numbers.
The numbers are 5 and 4.
Six times a number plus twice a second number is four. Twice the first number plus four times the second number is eighteen. Find the numbers.
Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen. Find the numbers.
The numbers are 2 and 3.
Twice a number plus three times a second number is negative one. The first number plus four times the second number is two. Find the numbers.
A married couple together earn $75,000. The husband earns $15,000 more than five times what his wife earns. What does the wife earn?
$10,000
During two years in college, a student earned $9,500. The second year she earned $500 more than twice the amount she earned the first year. How much did she earn the first year?
Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was $5000 more than twice the amount she put into the CD. How much did she invest in each account?
She put $15,000 into a CD and $35,000 in bonds.
Jorge invested $28,000 into two accounts. The amount he put in his money market account was $2,000 less than twice what he put into a CD. How much did he invest in each account?
In her last two years in college, Marlene received $42,000 in loans. The first year she received a loan that was $6,000 less than three times the amount of the second year’s loan. What was the amount of her loan for each year?
The amount of the first year’s loan was $30,000 and the amount of the second year’s loan was $12,000.
Jen and David owe $22,000 in loans for their two cars. The amount of the loan for Jen’s car is $2000 less than twice the amount of the loan for David’s car. How much is each car loan?
Solve Direct Translation Applications
In the following exercises, translate to a system of equations and solve.
Alyssa is twelve years older than her sister, Bethany. The sum of their ages is forty-four. Find their ages.
Bethany is 16 years old and Alyssa is 28 years old.
Robert is 15 years older than his sister, Helen. The sum of their ages is sixty-three. Find their ages.
The age of Noelle’s dad is six less than three times Noelle’s age. The sum of their ages is seventy-four. Find their ages.
Noelle is 20 years old and her dad is 54 years old.
The age of Mark’s dad is 4 less than twice Marks’s age. The sum of their ages is ninety-five. Find their ages.
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